Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T05:42:21.289Z Has data issue: false hasContentIssue false

On Rings whose Simple Modules are Flat

Published online by Cambridge University Press:  20 November 2018

Yasuyuki Hirano*
Affiliation:
Department of Mathematics, Okayama University Okayama 700 Japan
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 ring R is called a right SF-ring if all of its simple right R-modules are flat. It is well known that a von Neumann regular ring is a right SF-ring. In this paper we study conditions under which the converse holds.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Baccella, G., Von Neumann regularity of V-rings with artinian primitive factor rings, Proc. Amer. Math. Soc. 103(1988), 747749.Google Scholar
2. Bass, H., Finitistic dimension and homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95(1960), 466488.Google Scholar
3. Chen, J., On von Neumann regular rings and SF-rings, Math. Japon. 36(1991), 11231127.Google Scholar
4. Fields, K. L., On the global dimension of residue rings, Pacific J. Math. 32(1970), 345349.Google Scholar
5. Kaplansky, I., Rings with a polynomial identity, Bull. Amer. Math. Math. Soc. 54(1948), 575580.Google Scholar
6. Kaplansky, I., Fields and Rings, University of Chicago Press, Chicago, 1972.Google Scholar
7. Lambek, J., Lectures on Rings and Modules, Blaisdell, Waltham, Massachusetts, 1966.Google Scholar
8. Michler, G. and Villamayor, O. E., On rings whose simple modules are injective, J. Algebra 25(1973), 185— 201.Google Scholar
9. Ramamurthi, V. S., On the injectivity and flatness of certain cyclic modules, Proc. Amer. Math. Soc. 48(1975), 2125.Google Scholar
10. Rege, M. B., On von Neumann regular rings and SF-rings, Math. Japon. 31(1986), 927936.Google Scholar
11. Rotman, J. J., An Introduction to Homological Algebra, Academic Press, New York, San Francisco, London, 1979.Google Scholar
12. Stenström, B., Rings of Quotients, Springer- Verlag, Berlin, Heidelberg, New York, 1975.Google Scholar
13. Xu, J., Flatness and injectivity of simple modules over a commutative ring, Comm. Algebra 19(1991), 535537.Google Scholar
14. Yue, R. Ming, Chi, On V-rings and prime rings, J. Algebra 62(1980), 1320.Google Scholar