International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 311-316
Classical quotient rings of generalized matrix rings
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 with identity is a generalized matrix ring with idempotent
set if is a finite set of orthogonal idempotents of whose sum is . We show that, in the
presence of certain annihilator conditions, such a ring is semiprime right Goldie if and only if
is semiprime right Goldie for all , and we calculate the classical right quotient ring of .