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

Classical quotient rings of generalized matrix rings