Hossein Mohammadzadeh Saany | ZAHEDAN (original) (raw)

Papers by Hossein Mohammadzadeh Saany

Research paper thumbnail of On a generalization of condition (E

Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of S... more Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of St. Andrews, 1998, pp. 72-77] introduced Condition (P E) which is a generalization of Condition (P) and showed that Condition (P E) implies weak flatness, but not the converse. In [A. Golchin and H. Mohammadzadeh, On homological classification of monoids by Condition (P E) of right acts, Italian J. Pure Appl. Math. 25 (2009) 175-186] characterized monoids by this condition of their acts. In this paper, we first introduce Condition (E E), which is a generalization of Condition (E) and then give a characterization of monoids by this condition of their (cyclic, Rees factor) acts. Also, we give a necessary and sufficient condition under which Condition (E E) coincides with Condition (P) (respectively, pullback flatness, strong flatness) of acts. Furthermore, many known results are generalized.

Research paper thumbnail of On the property <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>U</mi></mrow><annotation encoding="application/x-tex">U</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span></span></span></span>-($G$-$PWP$) of acts

Categories and General Algebraic Structures with Application, 2018

In this paper first of all we introduce Property U-(G-P W P) of acts, which is an extension of Co... more In this paper first of all we introduce Property U-(G-P W P) of acts, which is an extension of Condition (G-P W P) and give some general properties. Then we give a characterization of monoids when this property of acts implies some others. Also we show that the strong faithfulness (Pcyclicity) and (P-)regularity of acts imply the property U-(G-P W P). Finally, we give a necessary and sufficient condition under which all cyclic (finitely generated) right acts or all (strongly,-) torsion free cyclic (finitely generated) right acts satisfy Property U-(G-P W P).

Research paper thumbnail of On Condition (P′)

Semigroup Forum, Oct 9, 2012

In this paper we introduce a new flatness property of acts over monoids which is an extension of ... more In this paper we introduce a new flatness property of acts over monoids which is an extension of Conditions (P) and (E), called Condition (EP) and will give a classification of monoids over which all (finitely generated, cyclic, monocyclic) right acts satisfying Condition (EP) have other flatness properties and also monoids over which all (cyclic) right acts satisfy Condition (EP).

Research paper thumbnail of ON HOMOLOGICAL CLASSIFICATION OF MONOIDS BY CONDITION ＄(E^{￥prime})＄ OF RIGHT ACTS

The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学, 2007

Valdis Laan in (On a generalization of strong flatness, Acta Comment. Univ. Tartuensis 2 (1998), ... more Valdis Laan in (On a generalization of strong flatness, Acta Comment. Univ. Tartuensis 2 (1998), 55-60.) introduced Condition (Eprime)(E^{\prime})(Eprime) , a generalization of Condition (E)(E)(E) . In this paper we continue the investigation of Condition (Eprime)(E^{\prime})(Eprime) and give a classification of monoids by comparing this condition of their acts with other properties. We give also a classffication of monoids for which all (monocyclic, cyclic) right acts satisfy Condition (Eprime)(E^{\prime})(Eprime) and in particular for idempotent monoids and monoids SSS with E(S)=1E(S)=\{1\}E(S)=1 . A classification of monoids over which all monocyclic right acts are weakly pullback flat will be given too.

Research paper thumbnail of Exact Sequence of Semigroups

In this paper we introduce the concept of exact sequences of semigroups, and then focus on specic... more In this paper we introduce the concept of exact sequences of semigroups, and then focus on specic modes of them and after this we review some important features exiting in semigroups in such sequences.

Research paper thumbnail of On deleted diagonal acts of completely (0-) simple semigroups

Asian-European Journal of Mathematics, 2016

If [Formula: see text] is a semigroup without identity, then the deleted diagonal act of [Formula... more If [Formula: see text] is a semigroup without identity, then the deleted diagonal act of [Formula: see text] is the right [Formula: see text]-act [Formula: see text]. In [S. Bulman-Fleming and A. Gilmour, Flatness properties of diagonal acts over monoids, Semigroup Forum 79 (2009) 298–314] the authors answered the question of when [Formula: see text] is flat, satisfies Condition [Formula: see text] or [Formula: see text] for a completely [Formula: see text] simple semigroup (always represented here in regular Rees matrix form). In this paper we answer similar question for some other properties. There are also some results that can arise.

Research paper thumbnail of On GP-Flatness Property

It is well-known that, using principal weak flatness property, some important monoids are charact... more It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we recall a generalization of principal weak flatness called GP-flatness, and characterize monoids by this property of their right (Rees factor) acts. Also we investigate GP coherent monoids.

Research paper thumbnail of On Homological Classification of Monoids by Condition (E′ P) of Right S-acts

Asian-European Journal of Mathematics

Research paper thumbnail of On a generalization of weak flatness

Asian-european Journal of Mathematics, 2021

Laan in Pullbacks and flatness properties of acts I, [Commun. Algebra 29(2) (2001) 829–850] intro... more Laan in Pullbacks and flatness properties of acts I, [Commun. Algebra 29(2) (2001) 829–850] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. Golchin and Mohammadzadeh in [On Condition ([Formula: see text]), Semigroup Forum 86(2) (2012) 413–430] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. In this paper similarly, we introduce a generalization of weak flatness property, called [Formula: see text], and will classify monoids by this property of their acts. We also characterize [Formula: see text] coherent monoids in general and monoids coming from some special classes.

Research paper thumbnail of On homological classification of monoids by condition (E ' ) of right acts

Research paper thumbnail of On condition ( PWP E )

Southeast Asian Bulletin of Mathematics

Research paper thumbnail of On Properties of Product Acts over Monoids

Communications in Algebra, 2015

ABSTRACT

Research paper thumbnail of On strongly (P)-cyclic acts

Czechoslovak Mathematical Journal, 2009

By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we... more By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong (P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.

Research paper thumbnail of On Regularity of Acts

Research paper thumbnail of On R-Right (L-Left) Cancellative and Weakly R(L)-Cancellative Semigroups

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellati... more In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak R(L)-cancellativity.

Research paper thumbnail of On condition (EP)

Research paper thumbnail of On the U-WPF Acts over Monoids

journal of sciences islamic republic of iran, 2007

Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatn... more Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regularity and strong faithfulness of acts both imply U-WPF. An equivalent of that over monoids for which torsion freeness implies U-WPF is given too.

Research paper thumbnail of On a generalization of condition (E)

Asian-European Journal of Mathematics

Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of S... more Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of St. Andrews, 1998, pp. 72–77] introduced Condition [Formula: see text] which is a generalization of Condition [Formula: see text] and showed that Condition [Formula: see text] implies weak flatness, but not the converse. In [A. Golchin and H. Mohammadzadeh, On homological classification of monoids by Condition [Formula: see text] of right acts, Italian J. Pure Appl. Math. 25 (2009) 175–186] characterized monoids by this condition of their acts. In this paper, we first introduce Condition [Formula: see text], which is a generalization of Condition [Formula: see text] and then give a characterization of monoids by this condition of their (cyclic, Rees factor) acts. Also, we give a necessary and sufficient condition under which Condition [Formula: see text] coincides with Condition [Formula: see text] (respectively, pullback flatness, strong flatness) of acts. Furthermore, many known results...

Research paper thumbnail of Classification of monoids by Condition <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>P</mi><mi>W</mi><msub><mi>P</mi><mrow><mi>s</mi><mi>s</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(PWP_{ssc})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ssc</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>

Categories and General Algebraic Structures with Application, 2020

Condition (P W P) which was introduced by Laan is related to the concept of flatness of acts over... more Condition (P W P) which was introduced by Laan is related to the concept of flatness of acts over monoids. Golchin and Mohammadzadeh introduced Condition (P W PE) as a generalization of Condition (P W P). In this paper, we introduce Condition (P W Pssc) which is much easier to check than Conditions (P W P) and (P W PE) and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition (P W Pssc) will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition (P W Pssc) and also a classification of monoids S will be given for which all right S-acts satisfying some other flatness properties have Condition (P W Pssc).

Research paper thumbnail of Preservation of Rees exact sequences

Mathematica Slovaca, 2019

Yuqun Chen and K. P. Shum in [Rees short exact sequence of S-systems, Semigroup Forum 65 (2002), ... more Yuqun Chen and K. P. Shum in [Rees short exact sequence of S-systems, Semigroup Forum 65 (2002), 141–148] introduced Rees short exact sequence of acts and considered conditions under which a Rees short exact sequence of acts is left and right split, respectively. To our knowledge, conditions under which the induced sequences by functors Hom(RLS, –), Hom(–, RLS) and AS ⊗ S– (where R, S are monoids) are exact, are unknown. This article addresses these conditions. Results are different from that of modules.

Research paper thumbnail of On a generalization of condition (E

Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of S... more Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of St. Andrews, 1998, pp. 72-77] introduced Condition (P E) which is a generalization of Condition (P) and showed that Condition (P E) implies weak flatness, but not the converse. In [A. Golchin and H. Mohammadzadeh, On homological classification of monoids by Condition (P E) of right acts, Italian J. Pure Appl. Math. 25 (2009) 175-186] characterized monoids by this condition of their acts. In this paper, we first introduce Condition (E E), which is a generalization of Condition (E) and then give a characterization of monoids by this condition of their (cyclic, Rees factor) acts. Also, we give a necessary and sufficient condition under which Condition (E E) coincides with Condition (P) (respectively, pullback flatness, strong flatness) of acts. Furthermore, many known results are generalized.

Research paper thumbnail of On the property <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>U</mi></mrow><annotation encoding="application/x-tex">U</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">U</span></span></span></span>-($G$-$PWP$) of acts

Categories and General Algebraic Structures with Application, 2018

In this paper first of all we introduce Property U-(G-P W P) of acts, which is an extension of Co... more In this paper first of all we introduce Property U-(G-P W P) of acts, which is an extension of Condition (G-P W P) and give some general properties. Then we give a characterization of monoids when this property of acts implies some others. Also we show that the strong faithfulness (Pcyclicity) and (P-)regularity of acts imply the property U-(G-P W P). Finally, we give a necessary and sufficient condition under which all cyclic (finitely generated) right acts or all (strongly,-) torsion free cyclic (finitely generated) right acts satisfy Property U-(G-P W P).

Research paper thumbnail of On Condition (P′)

Semigroup Forum, Oct 9, 2012

In this paper we introduce a new flatness property of acts over monoids which is an extension of ... more In this paper we introduce a new flatness property of acts over monoids which is an extension of Conditions (P) and (E), called Condition (EP) and will give a classification of monoids over which all (finitely generated, cyclic, monocyclic) right acts satisfying Condition (EP) have other flatness properties and also monoids over which all (cyclic) right acts satisfy Condition (EP).

Research paper thumbnail of ON HOMOLOGICAL CLASSIFICATION OF MONOIDS BY CONDITION ＄(E^{￥prime})＄ OF RIGHT ACTS

The Yokohama mathematical journal = 横濱市立大學紀要. D部門, 数学, 2007

Valdis Laan in (On a generalization of strong flatness, Acta Comment. Univ. Tartuensis 2 (1998), ... more Valdis Laan in (On a generalization of strong flatness, Acta Comment. Univ. Tartuensis 2 (1998), 55-60.) introduced Condition (Eprime)(E^{\prime})(Eprime) , a generalization of Condition (E)(E)(E) . In this paper we continue the investigation of Condition (Eprime)(E^{\prime})(Eprime) and give a classification of monoids by comparing this condition of their acts with other properties. We give also a classffication of monoids for which all (monocyclic, cyclic) right acts satisfy Condition (Eprime)(E^{\prime})(Eprime) and in particular for idempotent monoids and monoids SSS with E(S)=1E(S)=\{1\}E(S)=1 . A classification of monoids over which all monocyclic right acts are weakly pullback flat will be given too.

Research paper thumbnail of Exact Sequence of Semigroups

In this paper we introduce the concept of exact sequences of semigroups, and then focus on specic... more In this paper we introduce the concept of exact sequences of semigroups, and then focus on specic modes of them and after this we review some important features exiting in semigroups in such sequences.

Research paper thumbnail of On deleted diagonal acts of completely (0-) simple semigroups

Asian-European Journal of Mathematics, 2016

If [Formula: see text] is a semigroup without identity, then the deleted diagonal act of [Formula... more If [Formula: see text] is a semigroup without identity, then the deleted diagonal act of [Formula: see text] is the right [Formula: see text]-act [Formula: see text]. In [S. Bulman-Fleming and A. Gilmour, Flatness properties of diagonal acts over monoids, Semigroup Forum 79 (2009) 298–314] the authors answered the question of when [Formula: see text] is flat, satisfies Condition [Formula: see text] or [Formula: see text] for a completely [Formula: see text] simple semigroup (always represented here in regular Rees matrix form). In this paper we answer similar question for some other properties. There are also some results that can arise.

Research paper thumbnail of On GP-Flatness Property

It is well-known that, using principal weak flatness property, some important monoids are charact... more It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we recall a generalization of principal weak flatness called GP-flatness, and characterize monoids by this property of their right (Rees factor) acts. Also we investigate GP coherent monoids.

Research paper thumbnail of On Homological Classification of Monoids by Condition (E′ P) of Right S-acts

Asian-European Journal of Mathematics

Research paper thumbnail of On a generalization of weak flatness

Asian-european Journal of Mathematics, 2021

Laan in Pullbacks and flatness properties of acts I, [Commun. Algebra 29(2) (2001) 829–850] intro... more Laan in Pullbacks and flatness properties of acts I, [Commun. Algebra 29(2) (2001) 829–850] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. Golchin and Mohammadzadeh in [On Condition ([Formula: see text]), Semigroup Forum 86(2) (2012) 413–430] introduced Condition [Formula: see text], a generalization of Condition [Formula: see text]. In this paper similarly, we introduce a generalization of weak flatness property, called [Formula: see text], and will classify monoids by this property of their acts. We also characterize [Formula: see text] coherent monoids in general and monoids coming from some special classes.

Research paper thumbnail of On homological classification of monoids by condition (E ' ) of right acts

Research paper thumbnail of On condition ( PWP E )

Southeast Asian Bulletin of Mathematics

Research paper thumbnail of On Properties of Product Acts over Monoids

Communications in Algebra, 2015

ABSTRACT

Research paper thumbnail of On strongly (P)-cyclic acts

Czechoslovak Mathematical Journal, 2009

By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we... more By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong (P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property of their right (Rees factor) acts.

Research paper thumbnail of On Regularity of Acts

Research paper thumbnail of On R-Right (L-Left) Cancellative and Weakly R(L)-Cancellative Semigroups

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellati... more In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak R(L)-cancellativity.

Research paper thumbnail of On condition (EP)

Research paper thumbnail of On the U-WPF Acts over Monoids

journal of sciences islamic republic of iran, 2007

Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatn... more Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regularity and strong faithfulness of acts both imply U-WPF. An equivalent of that over monoids for which torsion freeness implies U-WPF is given too.

Research paper thumbnail of On a generalization of condition (E)

Asian-European Journal of Mathematics

Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of S... more Golchin and Renshaw in [A flatness property of acts over monoid, Conf. Semigroup, University of St. Andrews, 1998, pp. 72–77] introduced Condition [Formula: see text] which is a generalization of Condition [Formula: see text] and showed that Condition [Formula: see text] implies weak flatness, but not the converse. In [A. Golchin and H. Mohammadzadeh, On homological classification of monoids by Condition [Formula: see text] of right acts, Italian J. Pure Appl. Math. 25 (2009) 175–186] characterized monoids by this condition of their acts. In this paper, we first introduce Condition [Formula: see text], which is a generalization of Condition [Formula: see text] and then give a characterization of monoids by this condition of their (cyclic, Rees factor) acts. Also, we give a necessary and sufficient condition under which Condition [Formula: see text] coincides with Condition [Formula: see text] (respectively, pullback flatness, strong flatness) of acts. Furthermore, many known results...

Research paper thumbnail of Classification of monoids by Condition <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>P</mi><mi>W</mi><msub><mi>P</mi><mrow><mi>s</mi><mi>s</mi><mi>c</mi></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(PWP_{ssc})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">ssc</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>

Categories and General Algebraic Structures with Application, 2020

Condition (P W P) which was introduced by Laan is related to the concept of flatness of acts over... more Condition (P W P) which was introduced by Laan is related to the concept of flatness of acts over monoids. Golchin and Mohammadzadeh introduced Condition (P W PE) as a generalization of Condition (P W P). In this paper, we introduce Condition (P W Pssc) which is much easier to check than Conditions (P W P) and (P W PE) and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition (P W Pssc) will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition (P W Pssc) and also a classification of monoids S will be given for which all right S-acts satisfying some other flatness properties have Condition (P W Pssc).

Research paper thumbnail of Preservation of Rees exact sequences

Mathematica Slovaca, 2019

Yuqun Chen and K. P. Shum in [Rees short exact sequence of S-systems, Semigroup Forum 65 (2002), ... more Yuqun Chen and K. P. Shum in [Rees short exact sequence of S-systems, Semigroup Forum 65 (2002), 141–148] introduced Rees short exact sequence of acts and considered conditions under which a Rees short exact sequence of acts is left and right split, respectively. To our knowledge, conditions under which the induced sequences by functors Hom(RLS, –), Hom(–, RLS) and AS ⊗ S– (where R, S are monoids) are exact, are unknown. This article addresses these conditions. Results are different from that of modules.