Functional identities of degree 2 in triangular rings

Eremita, Daniel

doi:10.1016/j.laa.2012.07.028

Cited by 27 publications

(7 citation statements)

References 8 publications

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“…The classical examples of triangular rings are upper triangular matrix rings and nest algebras (see [5,12]). The centre of Q ml (R) is Moreover, there exists a unique ring isomorphism τ :…”

Section: The Main Resultsmentioning

confidence: 99%

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Biderivations of triangular rings

Wang

2015

Linear and Multilinear Algebra

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In this paper, we prove that every biderivation of certain triangular rings is the sum of an extremal biderivation and an inner biderivation, using the notion of maximal left ring of quotients. As a consequence, we show that every biderivation of the ring of all n × n upper triangular matrices over a unital ring (n ≥ 3) is the sum of an extremal biderivation and an inner biderivation, which extends two results of Benkovič and Ghosseiri, respectively.

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Section: The Main Resultsmentioning

confidence: 99%

“…In 2013, Eremita [12] initiated the study of functional identities of degree 2 in certain triangular rings. Recently, Eremita [13] investigated functional identities of degree 2 for a much wide class of triangular rings, using the notion of maximal left ring of quotients.…”

Section: Introductionmentioning

confidence: 99%

Biderivations of triangular rings

Wang

2015

Linear and Multilinear Algebra

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“…Zhang and his students [77] studied the functional identity (5.1) in the context of nest algebras. In two recent articles [39,40], Eremita considered functional identity (5.1) in triangular algebras. He managed to describe the form of additive mappings F 1 , F 2 , G 1 , G 2 : T −→ T satisfying (5.1) if a triangular ring T satisfies certain conditions.…”

Section: Topic For Future Researchmentioning

confidence: 99%

“…It is predictable that Eremita's approach, which is based on the notion of the maximal left ring of quotients, enable us to generalize and unify a number of known results regarding mappings of triangular algebras and generalized matrix algebras. The functional identities in triangular algebras and full matrix algebras were already studied in [5,23,39,40]. One would expect that the next step is to investigate functional identities of generalized matrix algebras.…”

Section: Topic For Future Researchmentioning

confidence: 99%

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

Liang

Wei

Xiao

et al. 2014

Linear and Multilinear Algebra

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Abstract. Let G be a generalized matrix algebra over a commutative ring R and Z(G) be the center of G. Suppose that q : G × G −→ G is an R-bilinear mapping and Tq : G −→ G is the trace of q. We describe the form of Tq satisfying the condition [Tq(G), G] ∈ Z(G) for all G ∈ G. The question of when Tq has the proper form is considered. Using the aforementioned trace function, we establish sufficient conditions for each Lie triple isomorphism of G to be almost standard. As applications we characterize Lie triple isomorphisms of full matrix algebras, of triangular algebras and of certain unital algebras with nontrivial idempotents. Some topics for future research closely related to our current work are proposed at the end of this article.

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“…Using another approach the authors in [3, Corollary 2.5] described f -derivations of a matrix algebra M n (F) over an algebraically closed field F. Triangular algebras are the typical examples of algebras, that are not d-free sets and therefore the general FI theory can not be used. So far the only general functional identity that was studied on triangular algebras was the FI of degree 2 (see [5,6]). …”

Section: Introductionmentioning

confidence: 99%