On T-nilpotence of a matrix set

Abstract

Let R be a ring and I be an arbitrary right T-nilpotent subset of R. In the paper it is proved that in this case the set of all n×n-matrices with entries in I is a right T-nilpotent subset of the ring of n×n-matrices with entries in R, where n 2 N. It is also showed that it is impossible to generalize this result for rings of matrices of infinite dimension.