Some facts about zero divisors of triangular infinite matrices

Roksana Krystyna Słowik

Vol. 20 No. 2 (2015)

Regular Articles

Some facts about zero divisors of triangular infinite matrices

Published 2015-09-20

Roksana Krystyna Słowik

Roksana Krystyna Słowik
Silesian University of Technology

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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.

Keywords

zero divisors in matrix rings, infinite matrices

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