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

Abdelfattah Haily; Mostafa Alaoui

Publicacions Matemàtiques (2001)

  • Volume: 45, Issue: 1, page 219-222
  • ISSN: 0214-1493

Abstract

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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.

How to cite

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Haily, Abdelfattah, and Alaoui, Mostafa. "Perfect rings for which the converse of Schur's lemma holds.." Publicacions Matemàtiques 45.1 (2001): 219-222. <http://eudml.org/doc/41426>.

@article{Haily2001,
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.},
author = {Haily, Abdelfattah, Alaoui, Mostafa},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de anillos; Módulos algebraicos; endomorphism rings; simple modules; perfect rings; converse of Schur's lemma; finite products of primary rings},
language = {eng},
number = {1},
pages = {219-222},
title = {Perfect rings for which the converse of Schur's lemma holds.},
url = {http://eudml.org/doc/41426},
volume = {45},
year = {2001},
}

TY - JOUR
AU - Haily, Abdelfattah
AU - Alaoui, Mostafa
TI - Perfect rings for which the converse of Schur's lemma holds.
JO - Publicacions Matemàtiques
PY - 2001
VL - 45
IS - 1
SP - 219
EP - 222
AB - 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.
LA - eng
KW - Teoría de anillos; Módulos algebraicos; endomorphism rings; simple modules; perfect rings; converse of Schur's lemma; finite products of primary rings
UR - http://eudml.org/doc/41426
ER -

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