Biderivations of triangular rings

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 x 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 Benkovic and Ghosseiri, respectively.