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Commutativity Criteria for a Factor Ring R/P Arising from P-Centralizers
Lahcen Oukhtite,Karim Bouchannafa,My Abdallah Idrissi 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.4
In this paper we consider a more general class of centralizers called I centralizers. More precisely, given a prime ideal P of an arbitrary ring R we establish a connection between certain algebraic identities involving a pair of P-left centralizers and the structure of the factor ring R/P.
SOME FUNCTIONAL IDENTITIES ARISING FROM DERIVATIONS
Abdellah Mamouni,Lahcen Oukhtite,Mohammed Zerra Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.1
This paper considers some functional identities related to derivations of a ring R and their action on the centre of R/P where P is a prime ideal of R. It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.
RELATIONSHIP BETWEEN THE STRUCTURE OF A QUOTIENT RING AND THE BEHAVIOR OF CERTAIN ADDITIVE MAPPINGS
Bouchannafa, Karim,Idrissi, Moulay Abdallah,Oukhtite, Lahcen Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
The principal aim of this paper is to study the connection between the structure of a quotient ring R/P and the behavior of special additive mappings of R. More precisely, we characterize the commutativity of R/P using derivations (generalized derivations) of R satisfying algebraic identities involving the prime ideal P. Furthermore, we provide examples to show that the various restrictions imposed in the hypothesis of our theorems are not superfluous.
COMMUTATIVITY WITH ALGEBRAIC IDENTITIES INVOLVING PRIME IDEALS
Mir, Hajar El,Mamouni, Abdellah,Oukhtite, Lahcen Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
The purpose of this paper is to study the structure of quotient rings R/P where R is an arbitrary ring and P is a prime ideal of R. Especially, we will establish a relationship between the structure of this class of rings and the behavior of derivations satisfying algebraic identities involving prime ideals. Furthermore, the characteristic of the quotient ring R/P has been determined in some situations.
RELATIONSHIP BETWEEN THE STRUCTURE OF A FACTOR RING R/P AND DERIVATIONS OF R
Karim Bouchannafa,Moulay Abdallah Idrissi,Lahcen Oukhtite 대한수학회 2023 대한수학회보 Vol.60 No.5
The purpose of this paper is to study the relationship between the structure of a factor ring $R/P$ and the behavior of some derivations of $R$. More precisely, we establish a connection between the commutativity of $R/P$ and derivations of $R$ satisfying specific identities involving the prime ideal $P$. Moreover, we provide an example to show that our results cannot be extended to semi-prime ideals.