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

Autores: Abdelfattah Haily, M. Alaoui
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 45, Nº 1, 2001, págs. 219-222
Idioma: inglés
DOI: 10.5565/publmat_45101_10
Títulos paralelos:
- Anillos perfectos para los que se verifica el inverso del lema de Schur
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Resumen
- 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