Biderivations of triangular rings

Abstract

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 upper triangular matrices over a unital ring () is the sum of an extremal biderivation and an inner biderivation, which extends two results of Benkovič and Ghosseiri, respectively.

Keywords:

• triangular ring
• upper triangular matrix ring
• biderivation
• maximal left ring of quotients

AMS Subject Classifications:

• 16W25
• 15A78
• 16S50

Notes

No potential conflict of interest was reported by the author.