The structure of n-commuting additive maps on Lie ideals of prime rings

Liu, Cheng-Kai; Pu, Yen-Fu

doi:10.1016/j.laa.2021.07.026

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…For infinite-dimensional algebras and algebras of sufficiently large dimensions this was proved earlier in [91]. We also mention the papers [93,100,101] in which certain important special cases are treated in more general settings.…”

Section: Generalized Functional Identitiesmentioning

confidence: 63%

Functional identities and their applications

Brešar

2023

Bull. Math. Sci.

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Section: Generalized Functional Identitiesmentioning

confidence: 63%

Functional identities and their applications

Brešar

2023

Bull. Math. Sci.

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“…Then, in [5], the n-commuting additive maps for n ≥ 2 are described under certain conditions on the prime rings, and in [28], this result is extended to the semiprime rings. We refer to [28,29] to see more details in this regard. Every Lie n-centralizer is a n-commuting linear maps, but the converse is not necessarily true (see Example 3.1), so the characterization of n-commuting linear maps in terms of Lie n-centralizers on certain algebras is of interest.…”

Section: Introductionmentioning

confidence: 99%

Lie centralizers and commutant preserving maps on generalized matrix algebras

Ghahramani¹,

Mokhtari²,

Feng³

2023

J. Algebra Appl.

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Let [Formula: see text] be a 2-torsion free unital generalized matrix algebra with center [Formula: see text], and [Formula: see text] be a linear mapping on [Formula: see text] satisfying the condition [Formula: see text] This paper is devoted to the study of the structure of [Formula: see text] under some mild assumptions on [Formula: see text]. We provide the necessary and sufficient conditions for [Formula: see text] to be in the form [Formula: see text] ([Formula: see text]), where [Formula: see text] and [Formula: see text] is a linear mapping. Then we apply our results to characterize linear mappings on [Formula: see text] that are commutant preservers or double commutant preservers.

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An Engel condition with two generalized derivations on Lie ideals of prime rings

Liu

2022

J. Algebra Appl.

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Let [Formula: see text] be a prime ring, let [Formula: see text] be a noncentral Lie ideal of [Formula: see text] and let [Formula: see text] be two generalized derivations of [Formula: see text]. In this paper, we characterize the structure of [Formula: see text] and all possible forms of [Formula: see text] and [Formula: see text] such that [Formula: see text] for all [Formula: see text], where [Formula: see text] are fixed positive integers. With this, several known results can be either deduced or generalized. In particular, we give a Lie ideal version of the theorem obtained by Lee and Zhou in [An identity with generalized derivations, J. Algebra Appl. 8 (2009) 307–317] and describe a more complete version of the theorem recently obtained by Dhara and De Filippis in [Engel conditions of generalized derivations on left ideals and Lie ideals in prime rings, Comm. Algebra 48 (2020) 154–167].

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The structure of n-commuting additive maps on Lie ideals of prime rings

Cited by 3 publications

References 42 publications

Functional identities and their applications

Functional identities and their applications

Lie centralizers and commutant preserving maps on generalized matrix algebras

An Engel condition with two generalized derivations on Lie ideals of prime rings

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