BRAHIM FAHID - Academia.edu (original) (raw)

Papers by BRAHIM FAHID

ANNALI DELL'UNIVERSITA' DI FERRARA

Filomat

In this paper, we investigate Jordan ?-derivations and Lie ?-derivations on path algebras. This w... more In this paper, we investigate Jordan ?-derivations and Lie ?-derivations on path algebras. This work is motivated by the one of Benkovic done on triangular algebras and the study of Jordan derivations and Lie derivations on path algebras done by Li and Wei. Namely, main results state that every Jordan ?-derivation is a ?-derivation and every Lie ?-derivation is of a standard form on a path algebra when the associated quiver is acyclic and finite.

Communications in Algebra

Acta Mathematica Vietnamica

경북대학교 자연과학대학 수학과, Jun 1, 2017

The Korean Mathematical Society, Oct 1, 2018

Bollettino dell'Unione Matematica Italiana, 2018

Georgian Mathematical Journal, 2018

Let R be a commutative ring with {1\neq 0}. We recall that a proper ideal I of R is called a weak... more Let R be a commutative ring with {1\neq 0}. We recall that a proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever {a,b,c\in R} and {0\not=abc\in I}, then {ab\in I} or {ac\in\sqrt{I}} or {bc\in\sqrt{I}}. In this paper, we introduce a new class of ideals that is closely related to the class of weakly 2-absorbing primary ideals. Let {I(R)} be the set of all ideals of R and let {\delta:I(R)\rightarrow I(R)} be a function. Then δ is called an expansion function of ideals of R if whenever {L,I,J} are ideals of R with {J\subseteq I}, then {L\subseteq\delta(L)} and {\delta(J)\subseteq\delta(I)}. Let δ be an expansion function of ideals of R. Then a proper ideal I of R (i.e., {I\not=R}) is called a weakly 2-absorbing δ-primary ideal if {0\not=abc\in I} implies {ab\in I} or {ac\in\delta(I)} or {bc\in\delta(I)}. For example, let {\delta:I(R)\rightarrow I(R)} such that {\delta(I)=\sqrt{I}}. Then δ is an expansion function of ideals of R, and hence a proper ideal I o...

DESALINATION AND WATER TREATMENT

Mediterranean Journal of Mathematics, 2017

The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear ma... more The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear maps including derivations, Lie derivations and Jordan derivations. In this paper we introduce the notion of f-biderivations as a natural "biderivation" counterpart of the notion of "f-derivations". We first show, under some conditions, that any f-derivation is a Jordan biderivation. Then, we turn to study f-biderivations of a unital algebra with an idempotent. Our second main result shows, under some conditions, that every Jordan biderivation can be written as a sum of a biderivation, an antibiderivation and an extremal biderivation. As a consequence we show that every Jordan biderivation on a triangular algebra is a biderivation.

Communications in Algebra, 2021

In this paper, we investigate Lie generalized derivations on bound quiver algebras associated wit... more In this paper, we investigate Lie generalized derivations on bound quiver algebras associated with a finite acyclic quiver. The first main result shows that every bound quiver algebra associated with a finite acyclic quiver has the properness Lie generalized derivation property. The second main result investigates the uniqueness property. Namely, among other things, we show that a bound quiver algebra associated with a finite acyclic quiver E has the uniqueness Lie generalized derivation property if and only if the quiver E does not contain any isolated vertex.

In this paper we prove, under certain condition, when R is a semiprime ring with suitable charact... more In this paper we prove, under certain condition, when R is a semiprime ring with suitable characteristic restrictions, that every nonzero (m,n)-Jordan triple centralizer (resp., (m,n)-Jordan triple derivation) is a two-sided centralizer (resp., a derivation which maps R into Z(R)). This give partial affirmative answers to two conjectures of Vukman.

In this paper, we introduce the notions of rough n-absorbing (n-absorbing primary) ideals and rou... more In this paper, we introduce the notions of rough n-absorbing (n-absorbing primary) ideals and rough fuzzy n-absorbing (n-absorbing primary) ideals in a ring, and give some properties of such ideals. Also, we discuss the relations between the upper and lower rough n-absorbing (n-absorbing primary) ideals and the upper and lower approximations of their homomorphism images.

In this paper we give an affirmative answer to two conjectures on generalized (m,n)(m,n)(m,n)-Jordan deri... more In this paper we give an affirmative answer to two conjectures on generalized (m,n)(m,n)(m,n)-Jordan derivations and generalized (m,n)(m,n)(m,n)-Jordan centralizers raised in [S. Ali and A. Fo\v{s}ner, \textit{On Generalized (m,n)(m, n)(m,n)-Derivations and Generalized (m,n)(m, n)(m,n)-Jordan Derivations in Rings,} Algebra Colloq. \textbf{21} (2014), 411--420] and [A. Fo\v{s}ner, \textit{A note on generalized (m,n)(m,n)(m,n)-Jordan centralizers,} Demonstratio Math. \textbf{46} (2013), 254--262]. Precisely, when RRR is a semiprime ring, we prove, under some suitable torsion restrictions, that every nonzero generalized (m,n)(m,n)(m,n)-Jordan derivation (resp., a generalized (m,n)(m,n)(m,n)-Jordan centralizer) is a derivation (resp., a two-sided centralizer).

Rendiconti del Circolo Matematico di Palermo Series 2, 2018

The main aim of this paper is to generalize some results of Dhara et al. in (Miskolc Math Notes 1... more The main aim of this paper is to generalize some results of Dhara et al. in (Miskolc Math Notes 16:769–779, 2015) to the context of nonzero left ideals. We start the paper with a result which shows that any square closed Lie ideal of a 2-torsion free prime ring contains a nonzero ideal.

Rocky Mountain Journal of Mathematics, Dec 1, 2017

arXiv: Commutative Algebra, 2020

Let R be a commutative ring with identity. In this paper, we introduce the concept of (m, n)-clos... more Let R be a commutative ring with identity. In this paper, we introduce the concept of (m, n)-closed ideals of R and (m, n)-von Neumann regular rings

Communications in Algebra

ANNALI DELL'UNIVERSITA' DI FERRARA

Filomat

In this paper, we investigate Jordan ?-derivations and Lie ?-derivations on path algebras. This w... more In this paper, we investigate Jordan ?-derivations and Lie ?-derivations on path algebras. This work is motivated by the one of Benkovic done on triangular algebras and the study of Jordan derivations and Lie derivations on path algebras done by Li and Wei. Namely, main results state that every Jordan ?-derivation is a ?-derivation and every Lie ?-derivation is of a standard form on a path algebra when the associated quiver is acyclic and finite.

Communications in Algebra

Acta Mathematica Vietnamica

경북대학교 자연과학대학 수학과, Jun 1, 2017

The Korean Mathematical Society, Oct 1, 2018

Bollettino dell'Unione Matematica Italiana, 2018

Georgian Mathematical Journal, 2018

Let R be a commutative ring with {1\neq 0}. We recall that a proper ideal I of R is called a weak... more Let R be a commutative ring with {1\neq 0}. We recall that a proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever {a,b,c\in R} and {0\not=abc\in I}, then {ab\in I} or {ac\in\sqrt{I}} or {bc\in\sqrt{I}}. In this paper, we introduce a new class of ideals that is closely related to the class of weakly 2-absorbing primary ideals. Let {I(R)} be the set of all ideals of R and let {\delta:I(R)\rightarrow I(R)} be a function. Then δ is called an expansion function of ideals of R if whenever {L,I,J} are ideals of R with {J\subseteq I}, then {L\subseteq\delta(L)} and {\delta(J)\subseteq\delta(I)}. Let δ be an expansion function of ideals of R. Then a proper ideal I of R (i.e., {I\not=R}) is called a weakly 2-absorbing δ-primary ideal if {0\not=abc\in I} implies {ab\in I} or {ac\in\delta(I)} or {bc\in\delta(I)}. For example, let {\delta:I(R)\rightarrow I(R)} such that {\delta(I)=\sqrt{I}}. Then δ is an expansion function of ideals of R, and hence a proper ideal I o...

DESALINATION AND WATER TREATMENT

Mediterranean Journal of Mathematics, 2017

The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear ma... more The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear maps including derivations, Lie derivations and Jordan derivations. In this paper we introduce the notion of f-biderivations as a natural "biderivation" counterpart of the notion of "f-derivations". We first show, under some conditions, that any f-derivation is a Jordan biderivation. Then, we turn to study f-biderivations of a unital algebra with an idempotent. Our second main result shows, under some conditions, that every Jordan biderivation can be written as a sum of a biderivation, an antibiderivation and an extremal biderivation. As a consequence we show that every Jordan biderivation on a triangular algebra is a biderivation.

Communications in Algebra, 2021

In this paper, we investigate Lie generalized derivations on bound quiver algebras associated wit... more In this paper, we investigate Lie generalized derivations on bound quiver algebras associated with a finite acyclic quiver. The first main result shows that every bound quiver algebra associated with a finite acyclic quiver has the properness Lie generalized derivation property. The second main result investigates the uniqueness property. Namely, among other things, we show that a bound quiver algebra associated with a finite acyclic quiver E has the uniqueness Lie generalized derivation property if and only if the quiver E does not contain any isolated vertex.

In this paper we prove, under certain condition, when R is a semiprime ring with suitable charact... more In this paper we prove, under certain condition, when R is a semiprime ring with suitable characteristic restrictions, that every nonzero (m,n)-Jordan triple centralizer (resp., (m,n)-Jordan triple derivation) is a two-sided centralizer (resp., a derivation which maps R into Z(R)). This give partial affirmative answers to two conjectures of Vukman.

In this paper, we introduce the notions of rough n-absorbing (n-absorbing primary) ideals and rou... more In this paper, we introduce the notions of rough n-absorbing (n-absorbing primary) ideals and rough fuzzy n-absorbing (n-absorbing primary) ideals in a ring, and give some properties of such ideals. Also, we discuss the relations between the upper and lower rough n-absorbing (n-absorbing primary) ideals and the upper and lower approximations of their homomorphism images.

In this paper we give an affirmative answer to two conjectures on generalized (m,n)(m,n)(m,n)-Jordan deri... more In this paper we give an affirmative answer to two conjectures on generalized (m,n)(m,n)(m,n)-Jordan derivations and generalized (m,n)(m,n)(m,n)-Jordan centralizers raised in [S. Ali and A. Fo\v{s}ner, \textit{On Generalized (m,n)(m, n)(m,n)-Derivations and Generalized (m,n)(m, n)(m,n)-Jordan Derivations in Rings,} Algebra Colloq. \textbf{21} (2014), 411--420] and [A. Fo\v{s}ner, \textit{A note on generalized (m,n)(m,n)(m,n)-Jordan centralizers,} Demonstratio Math. \textbf{46} (2013), 254--262]. Precisely, when RRR is a semiprime ring, we prove, under some suitable torsion restrictions, that every nonzero generalized (m,n)(m,n)(m,n)-Jordan derivation (resp., a generalized (m,n)(m,n)(m,n)-Jordan centralizer) is a derivation (resp., a two-sided centralizer).

Rendiconti del Circolo Matematico di Palermo Series 2, 2018

The main aim of this paper is to generalize some results of Dhara et al. in (Miskolc Math Notes 1... more The main aim of this paper is to generalize some results of Dhara et al. in (Miskolc Math Notes 16:769–779, 2015) to the context of nonzero left ideals. We start the paper with a result which shows that any square closed Lie ideal of a 2-torsion free prime ring contains a nonzero ideal.

Rocky Mountain Journal of Mathematics, Dec 1, 2017

arXiv: Commutative Algebra, 2020

Let R be a commutative ring with identity. In this paper, we introduce the concept of (m, n)-clos... more Let R be a commutative ring with identity. In this paper, we introduce the concept of (m, n)-closed ideals of R and (m, n)-von Neumann regular rings

Communications in Algebra