f-Biderivations and Jordan biderivations of unital algebras with idempotents

25 Jan 2020  ·  Bahmani Mohammad Ali, Bennis Driss, Vishki Hamid Reza Ebrahimi, Fahid Brahim ·

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-derivation 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. read more

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Rings and Algebras