# Decomposition of algebra over a commutative artinian ring

Hi I am looking for a result about the following elementary question:

Suppose $A$ is an algebra and its center $C$ is an Artinian ring. It is well known that $C$ can be decomposed into a product of local Artinian rings: $C \cong C_1 \times \cdots \times C_t$. Would this decomposition lead to a certain decomposition of the algebra $A$? If so, I'd to konw a reference about this. Thanks

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Every algebra over a finite product of commutative rings is a product of algebras over the factors (just use the idempotents of the ring to split the algebra). – Angelo Jul 6 '13 at 20:25
Thanks! Now I understand. – Leslie Wu Jul 8 '13 at 3:12