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Perfect rings for which the converse of Schur's lemma holds.

Abdelfattah HailyMostafa Alaoui — 2001

Publicacions Matemàtiques

If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.

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