International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 311-316

Classical quotient rings of generalized matrix rings

David G. Poole1 and Patrick N. Stewart2

1Department of Mathematics, Trent University, Ontario, Peterborough K9J 7B8, Canada
2Department of Mathematics, Statistics and Computing Science, Dalhousie University, Nova Scotia, Halifax B3H aJ5, Canada

Received 18 March 1993

Copyright © 1995 David G. Poole and Patrick N. Stewart. 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.


An associative ring R with identity is a generalized matrix ring with idempotent set E if E is a finite set of orthogonal idempotents of R whose sum is 1. We show that, in the presence of certain annihilator conditions, such a ring is semiprime right Goldie if and only if eRe is semiprime right Goldie for all eE, and we calculate the classical right quotient ring of R.