Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-28T19:29:33.330Z Has data issue: false hasContentIssue false

Homological properties of SF rings

Published online by Cambridge University Press:  17 April 2009

Ahmad Shamsuddin
Affiliation:
Department of Mathematics, American University of Beirut, Beirut, Lebanon e-mail: ahmad@layla.aub.edu.lb
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.

A ring R is said to left SF if all simple left R-modules are flat. We study some homological properties of such rings and find situations in which these become von Neumann regular.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Anderson, F.W. and Fuller, K.R., Rings and categories of modules (2nd edition), Graduate texts in mathematics (Springer-Verlag, Berlin, Heidelberg, New York, 1992).CrossRefGoogle Scholar
[2]Bourbaki, N., Elements of mathematics—commutative algebra, (Chapters 1–7) (Springer-Verlag, Berlin, Heidelberg, New York, 1989).Google Scholar
[3]Ding, Nanqing and Chen, Jianlong, ‘The homological dimensions of simple modules’, Bull. Austral. Math. Soc. 48 (1993), 265274.CrossRefGoogle Scholar
[4]Jain, S., ‘Flat and FP-injectivity’, Proc. Amer. Math. Soc. 41 (1973), 437442.CrossRefGoogle Scholar
[5], S., ‘On finitely generated flat modules II’, Math. Scand. 27 (1970), 105112.Google Scholar
[6]Yue Chi Ming, R., ‘On von Neuman regular rings–II’, Math. Scand. 39 (1976), 167170.CrossRefGoogle Scholar
[7]Morita, K., ‘Flat modules, injective modules and quotient rings’, Math. Z. 120 (1971), 2540.CrossRefGoogle Scholar
[8]Nsatăsescu, C., ‘Dimension globale des anneaux semi-artiniens’, C.R. Acad. Sci. Paris Sér. A–B 268 (1969), A685688.Google Scholar
[9]Ramamurthi, V.S., ‘On the injectivity and flatness of certain cyclic modules’, Proc Amer. Math. Soc. 48 (1975), 2125.CrossRefGoogle Scholar
[10]Tjukavkin, D.V., ‘Rings all of whose one sided ideals are generated by idempotents’, Comm. Algebra 17 (1989), 11931198.CrossRefGoogle Scholar
[11]Warfield, R.B., ‘Purity and algebraic compactness for modules’, Pacific. J. Math. 28 (1969), 699719.CrossRefGoogle Scholar
[12]Xino, Y., ‘SF rings and excellent extensions’, Canad. Math. Bull. 37 (1994), 24632471.Google Scholar
[13]Xiao, Y., ‘One sided SF rings with certain chain conditions’, Comm. Algebra 22 (1994), 272277.Google Scholar
[14]Zhang, Jule and Xianneng, Du, ‘von Neumann regularity of SF rings’, Comm. Algebra 21 (1993), 24452451.Google Scholar