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
• Títulos paralelos:
  • Anillos perfectos para los que se verifica el inverso del lema de Schur
• Enlaces
  • Texto completo
• 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