Generalized biderivations of nest algebras

Functional identities of degree 2 in triangular rings

“…Our main theorem also enables us to determine the form of generalized inner biderivations for a certain class of triangular rings. In particular, we extend the result of Zhang et al [9,Theorem 3.1] in the context of nest algebras.…”

“…Using this result he described the form of generalized inner biderivations of prime rings [5,Theorem 4.7]. Somewhat later, Zhang et al [9] considered functional identity (1.1) in nest algebras. They discovered that in a certain class of nest algebras functional identity (1.1) has only the standard solution.…”

On biderivations of upper triangular matrix rings

“…(vi) There exists an (R, S)-bimodule homomorphism f : M × M → M such that for all m, m ∈ M, r, r ∈ R, and s, s ∈ S we have d mE 12 , m E 12 = f m, m E 12 ; (14) r, r f m,…”

“…Also, Benkovič [1] proved that under certain conditions every biderivation of a triangular algebra decomposes into the sum of an inner biderivation and a special kind of biderivation which is called an extremal biderivation. More details on biderivations, their generalizations, and related maps can be found in [2,[5][6][7][8][9]12,14,15]. Specially, the reader is encouraged to read the survey paper of Brešar [2] in which he has described the applications of biderivations to some other fields.…”

Centralizing traces and Lie triple isomorphisms on generalized matrix algebras

“…Later, several problems on certain types of mappings on triangular rings and algebras have been studied, where some special examples of functional identities appear. 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.…”