On biderivations of upper triangular matrix rings

Let R and S be rings with identity, M be a unitary (R,S)-bimodule, and T=RM0S be the upper triangular matrix ring determined by R,S and M. Let Eij be the standard matrix unit. In this paper we show that every biderivation of T is decomposed into the sum of three biderivations D,Ψ and Δ, where D(E11,E11)=0,Ψ is an extremal biderivation and Δ is a special kind of biderivation. Using this characterization, we determine the structure of biderivations of the ring Tn(R)(n⩾2) of all n×n upper triangular matrices over R, and show that in the special case when R is a noncommutative prime ring, every biderivation of Tn(R) is inner. This extends some results of Benkovič (2009) [1].