Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T04:03:54.635Z Has data issue: false hasContentIssue false
  • English
  • Français

FPF Rings and Some Conjectures of C. Faith

Published online by Cambridge University Press:  20 November 2018

S. S. Page
S. S. Page*
Affiliation:
University of British Columbia, Vancouver, B.C. V6T 1W5
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.

A left FPF ring is a ring R such that every finitely generated faithful left R -module generates the category of left R-modules. It is shown that such rings split into R = A⊕B, where A is a two sided ideal, and A contains the left singular ideal of R as an essential submodule. If R is FPF on both sides B is two sided too, and R is the product of A and B. An example shows this is the best possible and that right FPF does not imply left FPF.

Keywords

16A 4816A 36Faithful generatorsFPFSingular idealself-injective rings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 257 - 259
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Azumaya, G., Completely faithful modules and self-injective rings, Nagoya Math. J. 27 (1966), 697-708. MR 35 #4253.Google Scholar
2. Faith, C., Injective quotient rings of commutative rings, Module Theory Lect. Notes in Math. 700, Springer-Verlag, Berlin, 151-203.Google Scholar
3. Faith, C., Results on the structure of FPF rings. To appear in Nagoya Math.Google Scholar
4. Lambek, J., Rings and Modules, Blaisdell, New York, 1966.Google Scholar
5. Osofsky, B., A generalization of quasi-Frobenius rings, J. Algebra, 4 (1966) 373-387.Google Scholar
6. Page, S., Regular FPF Rings, Pac. J. Math. Vol. 79, No. 1, 1978, 169-176.Google Scholar
7. Page, S., Semiprime and Nonsingular FPF rings. Comm. in Algebra, 10 #20 (1982).Google Scholar
8. Page, S., Semihereditary and Fully Idempotent FPF Rings. To appear in Comm. in Algebra.Google Scholar
9. Utumi, Y., On quotient rings, Osaka Math. J., 8 (1956), 1-18.Google Scholar
10. Utumi, Y., Self injective rings, J. Algebra, 6 (1967), 56-64.Google Scholar