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Compressible matrix rings

Let Z(K) denote the center of a ring K. A ring R is compressible if Z(eRe) = eZ(R) for each idempotent e of R. In response to a question of S. Berberian, G. Bergman has constructed a (non-commutative) integral domain, satisfying a polynomial identity, for which the 2×2 matrix ring over the domain is not compressible. In contrast to Bergman's example, we show that the ring of nxn matrices over any commutative ring is always compressible.