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}.