Lie generalized derivations on trivial extension algebras

Bennis, Driss; Vishki, Hamid Reza Ebrahimi; Fahid, Brahim; Khadem-Maboudi, Ali Akbar; Mokhtari, Amir Hosein

doi:10.1007/s40574-018-0177-x

Cited by 8 publications

(5 citation statements)

References 16 publications

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“…At this stage we remark that, triangular algebras are special examples of trivial extension algebras on which the Jordan generalized and Lie generalized derivations are recently investigated in [3,7]. We conclude this section with the following question, to the best of our knowledge, has not been studied/answered yet:…”

Section: Corollary 210 Every Jordan Biderivation On a Triangular Alge...mentioning

confidence: 95%

f-Biderivations and Jordan biderivations of unital algebras with idempotents

et al. 2020

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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 -biderivation 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.

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Section: Corollary 210 Every Jordan Biderivation On a Triangular Alge...mentioning

confidence: 95%

f-Biderivations and Jordan biderivations of unital algebras with idempotents

et al. 2020

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“…In 2018, Bahmani et al [3] studied Jordan generalized derivations on trivial extensions. Later, in 2019, Bennis et al [5] studied Lie generalized derivations on trivial extensions.…”

Section: Introductionmentioning

confidence: 99%

“…In 2018, Bahmani et al [3] studied Jordan generalized derivations on trivial extensions. Later, in 2019, Bennis et al [5] studied Lie generalized derivations on trivial extensions. In this paper, we present a comprehensive investigation of derivations, trivial extensions, and their interplay.…”

Section: Introductionmentioning

confidence: 99%

On derivations over trivial extensions

Boudine,

Zerra

2024

Proyecciones (Antofagasta)

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In this paper, we investigate the structure of derivations over trivial extensions. We provide a detailed analysis of the structure of derivations on trivial extensions, the centre of trivial extensions, and the conditions for a trivial extension to be prime. Additionally, we examine the structure of derivations on trivial extensions when the underlying ring, $R$, is a prime ring, under the conditions of Herstein's Theorem, Posner's Theorem, and Bell's theorem.

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“…Trivial extension algebras have been extensively studied in algebra and analysis (see [11][12][13][14][15][16]). In this paper, we will study the structure of Lie n-centralizers on a trivial extension algebra.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of Lie $n$ -Centralizers on Certain Trivial Extension Algebras

Li,

Yuan,

Zhang

2023

Journal of Mathematics

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In this paper, we describe the structure of Lie n -centralizers of a trivial extension algebra. We then present some conditions under which a Lie n -centralizer on a trivial extension algebra is proper. As an application, we consider Lie n -centralizers on a triangular algebra.

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Lie generalized derivations on trivial extension algebras

Cited by 8 publications

References 16 publications

f-Biderivations and Jordan biderivations of unital algebras with idempotents

f-Biderivations and Jordan biderivations of unital algebras with idempotents

On derivations over trivial extensions

Characterizations of Lie $n$ -Centralizers on Certain Trivial Extension Algebras

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Lie generalized derivations on trivial extension algebras

Cited by 8 publications

References 16 publications

f-Biderivations and Jordan biderivations of unital algebras with idempotents

f-Biderivations and Jordan biderivations of unital algebras with idempotents

On derivations over trivial extensions

Characterizations of Lie n -Centralizers on Certain Trivial Extension Algebras

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Product

Resources

About

Characterizations of Lie $n$ -Centralizers on Certain Trivial Extension Algebras