International Journal of Mathematics and Mathematical Sciences (Jan 2003)
Isomorphism of generalized triangular matrix-rings and recovery of tiles
Abstract
We prove an isomorphism theorem for generalized triangular matrix-rings, over rings having only the idempotents 0and 1, in particular, over indecomposable commutative rings or over local rings (not necessarily commutative). As a consequence, we obtain a recovery result for the tile in a tiled matrix-ring.