ELA, Volume 16, pp. 11-124, April 2007, abstract.

On Roth's Pseudo Equivalence Over Rings

Robert E. Hartwig and Pedro Patricio

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_{ii}X - YT_{jj} = U_{ij}.