International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 311-316
doi:10.1155/S0161171295000391
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
Abstract
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 e∈E, and we calculate the classical right quotient ring of R.