Geodesic
On Roth's pseudo equivalence over rings
The electronic journal of linear algebra, Tome 16 (2007), pp. 111-124.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The pseudo-equivalence of a block lower triangular matrix T = [Tij] over a regular ring and its block diagonal matrix $D(T )$ = [Tii] 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 TiiX - Y Tjj = Uij.
Classification : 16A30, 15A21
Keywords: regular rings, Roth equivalence 
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     author = {Hartwig, R.E. and Patricio, Pedro},
     title = {On {Roth's} pseudo equivalence over rings},
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Hartwig, R.E.; Patricio, Pedro. On Roth's pseudo equivalence over rings. The electronic journal of linear algebra, Tome 16 (2007), pp. 111-124. http://geodesic.mathdoc.fr/item/ELA_2007__16__a28/