Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

share|improve this question
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.