Classical quotient rings of generalized matrix rings

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.