Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T01:30:22.120Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Structure of Quotient Rings Which are QFX Rings

Published online by Cambridge University Press:  20 November 2018

Samuel L. Dunn
Samuel L. Dunn*
Affiliation:
School of Natural And Mathematical Sciences Seattle Pacific College, Seattle, Washington 98119
Rights & Permissions [Opens in a new window]

Extract

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.

The object of this paper is to consider the relationships between matrix rings and rings having classical quotient rings which are quasi-Frobenius X (QFX) rings. The main result of this paper is Theorem 12, which shows that if S is a ring with a QFX right classical quotient ring T, then T is isomorphic to a direct sum of a finite number of matrix rings over local rings Ui, while S is almost a direct sum of matrix rings over rings Ci, the Ui being right classical quotient rings of the Ci.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 203 - 207
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Dieudonne, J., Remarks on quasi-Frobenius rings, J. Math. 2 (1958), 346-354.Google Scholar
2. Faith, Carl, Orders in simple Artinian rings, Trans. Amer. Math. Soc. 114 (1965), 61-64.Google Scholar
3. Faith, Carl and Utumi, Yuzo, On Noetherianprime rings, Trans. Amer. Math. Soc. 114 (1965), 53-60.Google Scholar
4. Faith, Carl and Walker, E. A., Direct sum representations of infective modules, J. Algebra, 5 (1967), 203-221.Google Scholar
5. Feller, E. H., A type of Quasi-Frobenius ring, Canad. Math. Bull., 10 (1967), 19-27.Google Scholar
6. Goldie, A. W., Semi-prime rings with maximum condition, Proc. London Math. Soc. 10 (1960), 201-220.Google Scholar
7. Jans, J. P., On orders in Quasi-Frobenius rings, J. Algebra, 7 (1967), 35-43.Google Scholar
8. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass., 1966.Google Scholar
9. Small, Lace W., Orders in Artinian rings, J. Algebra, 4 (1966), 13-41; Correction and addendum, 4 (1966), 505-507.Google Scholar
10. Tsai, C., Report on injective modules, Queen's Papers in Pure and Applied Math., No. 6. Queen's University, Kingston, Ontario, 1966.Google Scholar
11. Zaks, Abraham, Quasi-Frobenius X-rings, unpublished, Technion Israel Institute of Technology, 1969.Google Scholar