International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 533-538
Isomorphism of generalized triangular matrix-rings and recovery of tiles
1Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
2Department of Mathematics, Stellenbosch University, Private Bag X1, Stellenbosch 7602, South Africa
Received 5 May 2002
Copyright © 2003 R. Khazal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove an isomorphism theorem for generalized triangular
matrix-rings, over rings having only the idempotents and , 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.