On Roth's pseudo equivalence over rings

Abstract

The pseudo-equivalence of a block lower triangular matrix T = [T_ij ] over a regular ring and its block diagonal matrix D(T)=[T_ii] is characterized in terms of suitable Roth consistency conditions. The latter can in turn be expressed in terms of the solvability of certain matrix equations of the form T_iiX − Y T_jj = U_ij .