Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T20:29:02.238Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of Left Perfect Rings

Published online by Cambridge University Press:  20 November 2018

Yiqiang Zhou
Yiqiang Zhou*
Affiliation:
Mathematics Department, University of British Columbia, Vancouver, British Columbia, V6T 1Z2
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

16L30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 382 - 384
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Anderson, F. W. and Fuller, K. R., Rings and Categories of Modules (second edition), Springer- Verlag, 1992.Google Scholar
2. Neggers, J., Cyclic rings, Rev. Un. Mat. Argentina 28(1977), 108–114.Google Scholar
3. Nashier, B. and Nichols, W., A note on perfect rings, Manuscripta Math. 70(1991), 307—310.Google Scholar
4. Rant, W. H., Minimally generated modules, Canad. Math. Bull. 23(1980), 103–105.Google Scholar
5. Stenström, B., Rings of Quotients, Springer-Verlag, 1975.Google Scholar