Perfect rings for which the converse of Schur's lemma holds
Haily, A. (Faculté des Sciences (El Jadida, Marroc). Département de Mathématiques et Informatique)
Alaoui, M. (Faculté des Sciences (El Jadida, Marroc). Département de Mathématiques et Informatique)
Date: |
2001 |
Abstract: |
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. |
Rights: |
Tots els drets reservats. |
Language: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Published in: |
Publicacions matemàtiques, V. 45 N. 1 (2001) , p. 219-222, ISSN 2014-4350 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/38014
DOI: 10.5565/PUBLMAT_45101_10
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Record created 2006-03-13, last modified 2022-02-20