Gholamreza Moghaddasi - Academia.edu (original) (raw)

Uploads

Papers by Gholamreza Moghaddasi

In this paper, we define the notion of regular prime monomorphism for SSS-posets over a pomonoid ... more In this paper, we define the notion of regular prime monomorphism for SSS-posets over a pomonoid SSS and investigate some categorical properties including products, coproducts and pullbacks. We study mathcalMmathcal{M}mathcalM-injectivity in the category of SSS-posets where mathcalMmathcal{M}mathcalM is the class of regular prime monomorphisms and show that the Skornjakov criterion fails for the regular prime injectivity. Considering a weaker form of such kind of injectivity, we obtain some classifications for pomonoids.

Journal of Nonlinear Sciences and Applications, 2012

In this paper using the notion of a sequentially dense monomorphism we consider sequential inject... more In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity (s-injectivity) for acts over a semigroup S. We show that s-injectivity, s-absolutely retract, and sequential compactness are equivalent.

In this paper, in addition to some elementary facts about the ultra-groups, which their structure... more In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an ultra-group over a group, there exists a normal subgroup of that certain group. Moreover, by proving this feature that a monomorphism in groups preserve the ultra-groups over groups, we show that, corresponding to any monomorphism in groups, there is an ultra-group homomorphism on the subgroups of those groups. Finally, we prove isomorphism theorems for ultra-groups. These theorems connect three notions subultra-group, normal subultra-group, quotient ultra-group, and directly, similar to the isomorphism theorems in group theory and module theory are proved.

Hacettepe Journal of Mathematics and Statistics, 2017

This article has been prepared based on a new concept of an ultra-group H M which is depend on a ... more This article has been prepared based on a new concept of an ultra-group H M which is depend on a group G and its subgroup H. Our aim is to introduce the category of ultra-groups and investigate about some properties of this category.

Bulletin of The Iranian Mathematical Society, 2017

‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some... more ‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some classes of semigroups‎, ‎such as zero‎ ‎semigroups‎, ‎right zero semigroups‎ ‎and strong chain of left zero semigroups.

Taiwanese Journal of Mathematics, 2011

The notion of sequential purity for acts over the monoid N ∞ , called projection algebras, was in... more The notion of sequential purity for acts over the monoid N ∞ , called projection algebras, was introduced and studied by Mahmoudi and Ebrahimi. This paper is devoted to the study of this notion and its relation to injectivity of S-acts for a semigroup S. We prove that in general injectivity implies absolute sequential purity and they are equivalent for acts over some classes of semigroups.

Journal of Algebraic Systems, Feb 1, 2015

In this paper we study the notions of cogenerator and subdirectly irreducible in the category of ... more In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-posets. First we give some necessary and sufficient conditions for an S-poset to be a cogenerator. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff's Representation Theorem for algebras, we study subdirectly irreducible S-posets and prove this theorem for the category of ordered right acts over an ordered monoid. Among other things, we present the relationship between cogenerators and subdirectly irreducible S-posets.

Abstract: Injectivity with respect to some subclasses of monomorphisms in a category has been stu... more Abstract: Injectivity with respect to some subclasses of monomorphisms in a category has been studied. In this article, we define the notion of regular poprime monomorphism in the category of S-posets with a monotone action of a pomonoid S on them and study M-injectivity where M is a subclass of regular poprime monomorphisms. More ever, we characterize their behaviour considered constructions such as the product, coproduct, direct sum, pullbacks, and pushouts of S-posets. The main purpose of this paper is to find a relation between regular poprime injective and poprime extensions of S-posets. چکیده مفهوم انژکتیوی یک شی در یک رسته‎‌ مفهوم انژکتیوی یک شی در یک رسته نسبت به رده‌های مختلفی از تکریختی‌های آن رسته همواره مورد مطالعه بوده ‌است. ما در این مقاله، مفهوم تکریختی‌های اول مرتب منظم را در رسته S-سیستم‌های مرتب جزیی روی تکواره مرتب جزیی S تعریف کرده‌ و به مطالعه M-انژکتیوی اشیاء آن رسته می‌پردازیم، که M یک رده‌ از تکریختی های اول مرتب منظم می‌باشد. بعلاوه، رفتار این تکریختی‌ها را ...

The main purpose of this paper is to construct the quotient ultra-groups, which are based on cong... more The main purpose of this paper is to construct the quotient ultra-groups, which are based on congruences. By these means we can present fundamental theorem and Lagrange theorem for the ultra-groups. Also, we show not necessary that the order of each element of the ultra-group divided by the order of the ultra-group.

Algebraic structures appear in most branches of mathematics, such as the abstract algebra, univer... more Algebraic structures appear in most branches of mathematics, such as the abstract algebra, universal algebra, varieties and category theory. The identification of algebraic structures is also useful in other fields of science. For instance recognition of algebraic structures in quantum physical systems has been an important tool for their understanding (see[4, 9]). Nowadays, answering to the new questions needs some more new tools. One of the very useful notions in mathematics as well as in computer science is the notion of s-acts (see [3, 5] for more details). We establish a new structure, ultragroup. The concept of an ultra-group is the base of a new branch of studies in algebra and the future researches. In the present work we continue the study of a variant of natural generalization of a notion of transversal in a group to its subgroup (see [1, 7]). In the next section of this article we define the notions which are useful through out this work such as a pair of subsets which ar...

Turkish Journal of Mathematics, 2012

The aim of this paper is to characterize subdirectly irreducible S-acts over left zero semigroups... more The aim of this paper is to characterize subdirectly irreducible S-acts over left zero semigroups. Also we compute the number of such acts and specify cogenerators acts over left zero semigroups. To do these we first take another look at the description of injective hulls of the separated S-acts over left zero semigroups.

In this paper we study the notions of cogenerator and subdirectly irreducible in the category of ... more In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-posets. First we give some necessary and sufficient conditions for an S-poset to be a cogenerator. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff’s Representation Theorem for algebras, we study subdirectly irreducible S-posets and prove this theorem for the category of ordered right acts over an ordered monoid. Among other things, we present the relationship between cogenerators and subdirectly irreducible S-posets.

In this paper, we intend to define an ultra-group by its presentation. The attitude of the presen... more In this paper, we intend to define an ultra-group by its presentation. The attitude of the presentation for a group was the key for us to investigate in this area. Instead of writing whole elements of an ultra-group, we denote it by its generators and the relations among those generators. A general computational approach for finitely presented ultra-groups by quotient ultra-groups and subultra-groups is described and some examples are presented. It is the way that can clarify the structure of an ultra-group quicker than having just a list of elements.

In this paper, we define the notion of regular prime monomorphism for SSS-posets over a pomonoid ... more In this paper, we define the notion of regular prime monomorphism for SSS-posets over a pomonoid SSS and investigate some categorical properties including products, coproducts and pullbacks. We study mathcalMmathcal{M}mathcalM-injectivity in the category of SSS-posets where mathcalMmathcal{M}mathcalM is the class of regular prime monomorphisms and show that the Skornjakov criterion fails for the regular prime injectivity. Considering a weaker form of such kind of injectivity, we obtain some classifications for pomonoids.

Journal of Nonlinear Sciences and Applications, 2012

In this paper using the notion of a sequentially dense monomorphism we consider sequential inject... more In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity (s-injectivity) for acts over a semigroup S. We show that s-injectivity, s-absolutely retract, and sequential compactness are equivalent.

In this paper, in addition to some elementary facts about the ultra-groups, which their structure... more In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an ultra-group over a group, there exists a normal subgroup of that certain group. Moreover, by proving this feature that a monomorphism in groups preserve the ultra-groups over groups, we show that, corresponding to any monomorphism in groups, there is an ultra-group homomorphism on the subgroups of those groups. Finally, we prove isomorphism theorems for ultra-groups. These theorems connect three notions subultra-group, normal subultra-group, quotient ultra-group, and directly, similar to the isomorphism theorems in group theory and module theory are proved.

Hacettepe Journal of Mathematics and Statistics, 2017

This article has been prepared based on a new concept of an ultra-group H M which is depend on a ... more This article has been prepared based on a new concept of an ultra-group H M which is depend on a group G and its subgroup H. Our aim is to introduce the category of ultra-groups and investigate about some properties of this category.

Bulletin of The Iranian Mathematical Society, 2017

‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some... more ‎In this paper‎, ‎we characterize and find the number of subdirectly‎ ‎irreducible acts over some classes of semigroups‎, ‎such as zero‎ ‎semigroups‎, ‎right zero semigroups‎ ‎and strong chain of left zero semigroups.

Taiwanese Journal of Mathematics, 2011

The notion of sequential purity for acts over the monoid N ∞ , called projection algebras, was in... more The notion of sequential purity for acts over the monoid N ∞ , called projection algebras, was introduced and studied by Mahmoudi and Ebrahimi. This paper is devoted to the study of this notion and its relation to injectivity of S-acts for a semigroup S. We prove that in general injectivity implies absolute sequential purity and they are equivalent for acts over some classes of semigroups.

Journal of Algebraic Systems, Feb 1, 2015

In this paper we study the notions of cogenerator and subdirectly irreducible in the category of ... more In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-posets. First we give some necessary and sufficient conditions for an S-poset to be a cogenerator. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff's Representation Theorem for algebras, we study subdirectly irreducible S-posets and prove this theorem for the category of ordered right acts over an ordered monoid. Among other things, we present the relationship between cogenerators and subdirectly irreducible S-posets.

Abstract: Injectivity with respect to some subclasses of monomorphisms in a category has been stu... more Abstract: Injectivity with respect to some subclasses of monomorphisms in a category has been studied. In this article, we define the notion of regular poprime monomorphism in the category of S-posets with a monotone action of a pomonoid S on them and study M-injectivity where M is a subclass of regular poprime monomorphisms. More ever, we characterize their behaviour considered constructions such as the product, coproduct, direct sum, pullbacks, and pushouts of S-posets. The main purpose of this paper is to find a relation between regular poprime injective and poprime extensions of S-posets. چکیده مفهوم انژکتیوی یک شی در یک رسته‎‌ مفهوم انژکتیوی یک شی در یک رسته نسبت به رده‌های مختلفی از تکریختی‌های آن رسته همواره مورد مطالعه بوده ‌است. ما در این مقاله، مفهوم تکریختی‌های اول مرتب منظم را در رسته S-سیستم‌های مرتب جزیی روی تکواره مرتب جزیی S تعریف کرده‌ و به مطالعه M-انژکتیوی اشیاء آن رسته می‌پردازیم، که M یک رده‌ از تکریختی های اول مرتب منظم می‌باشد. بعلاوه، رفتار این تکریختی‌ها را ...

The main purpose of this paper is to construct the quotient ultra-groups, which are based on cong... more The main purpose of this paper is to construct the quotient ultra-groups, which are based on congruences. By these means we can present fundamental theorem and Lagrange theorem for the ultra-groups. Also, we show not necessary that the order of each element of the ultra-group divided by the order of the ultra-group.

Algebraic structures appear in most branches of mathematics, such as the abstract algebra, univer... more Algebraic structures appear in most branches of mathematics, such as the abstract algebra, universal algebra, varieties and category theory. The identification of algebraic structures is also useful in other fields of science. For instance recognition of algebraic structures in quantum physical systems has been an important tool for their understanding (see[4, 9]). Nowadays, answering to the new questions needs some more new tools. One of the very useful notions in mathematics as well as in computer science is the notion of s-acts (see [3, 5] for more details). We establish a new structure, ultragroup. The concept of an ultra-group is the base of a new branch of studies in algebra and the future researches. In the present work we continue the study of a variant of natural generalization of a notion of transversal in a group to its subgroup (see [1, 7]). In the next section of this article we define the notions which are useful through out this work such as a pair of subsets which ar...

Turkish Journal of Mathematics, 2012

The aim of this paper is to characterize subdirectly irreducible S-acts over left zero semigroups... more The aim of this paper is to characterize subdirectly irreducible S-acts over left zero semigroups. Also we compute the number of such acts and specify cogenerators acts over left zero semigroups. To do these we first take another look at the description of injective hulls of the separated S-acts over left zero semigroups.

In this paper we study the notions of cogenerator and subdirectly irreducible in the category of ... more In this paper we study the notions of cogenerator and subdirectly irreducible in the category of S-posets. First we give some necessary and sufficient conditions for an S-poset to be a cogenerator. Then we see that under some conditions, regular injectivity implies generator and cogenerator. Recalling Birkhoff’s Representation Theorem for algebras, we study subdirectly irreducible S-posets and prove this theorem for the category of ordered right acts over an ordered monoid. Among other things, we present the relationship between cogenerators and subdirectly irreducible S-posets.

In this paper, we intend to define an ultra-group by its presentation. The attitude of the presen... more In this paper, we intend to define an ultra-group by its presentation. The attitude of the presentation for a group was the key for us to investigate in this area. Instead of writing whole elements of an ultra-group, we denote it by its generators and the relations among those generators. A general computational approach for finitely presented ultra-groups by quotient ultra-groups and subultra-groups is described and some examples are presented. It is the way that can clarify the structure of an ultra-group quicker than having just a list of elements.