A Characterization of Left Perfect Rings
Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 382-384
Voir la notice de l'article provenant de la source Cambridge University Press
In this note, we show that a ring R is a left perfect ring if and only if every generating set of each left R-module contains a minimal generating set. This result gives a positive answer to a question on left perfect rings raised by Nashier and Nichols.
Zhou, Yiqiang. A Characterization of Left Perfect Rings. Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 382-384. doi: 10.4153/CMB-1995-055-6
@article{10_4153_CMB_1995_055_6,
author = {Zhou, Yiqiang},
title = {A {Characterization} of {Left} {Perfect} {Rings}},
journal = {Canadian mathematical bulletin},
pages = {382--384},
year = {1995},
volume = {38},
number = {3},
doi = {10.4153/CMB-1995-055-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-055-6/}
}
[1] 1. Anderson, F. W. and Fuller, K. R., Rings and Categories of Modules (second edition), Springer- Verlag, 1992. Google Scholar
[2] 2. Neggers, J., Cyclic rings, Rev. Un. Mat. Argentina 28(1977), 108–114. Google Scholar
[3] 3. Nashier, B. and Nichols, W., A note on perfect rings, Manuscripta Math. 70(1991), 307—310. Google Scholar
[4] 4. Rant, W. H., Minimally generated modules, Canad. Math. Bull. 23(1980), 103–105. Google Scholar
[5] 5. Stenström, B., Rings of Quotients, Springer-Verlag, 1975. Google Scholar
Cité par Sources :