Some facts about zero divisors of triangular infinite matrices

Abstract

We are interested in the elements that are zero divisors in T_\infty(F) - the ring of N by N upper triangular matrices over a field F. It is known that a matrix from T_\infty(F) is a left zero divisor if and only if it contains at least one zero on the main diagonal. The problem when an infinite triangular matrix is a right zero divisor stays unsolved. In the paper we give some sufficient conditions for a matrix from T_\infty(F) to be a right zero divisor. We also present some properties of infinite matrices that help us in investigating the problem.