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A note on modules over regular rings

Published online by Cambridge University Press:  17 April 2009

K. M. Rangaswamy  and
N. Vanaja
K. M. Rangaswamy
Affiliation:
Madurai University, Madurai – 2 Tamil Nadu, India.
N. Vanaja
Affiliation:
Madurai University, Madurai – 2 Tamil Nadu, India.
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Abstract

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It is shown that a von Neumann regular ring R is left seif-injective if and only if every finitely generated torsion-free left R-module is projective. It is further shown that a countable self-injective strongly regular ring is Artin semi-simple.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 57 - 62
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Chase, Stephen U., “Direct products of modules”, Trans. Amer. Math. Soc. 97 (1960), 457–473.CrossRefGoogle Scholar
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[3]Pierce, R.S., “Modules over commutative regular rings”, Mem. Amer. Math. Soc. No. 70 (Amer. Math. Soc., Providence, Rhode Island; 1967).Google Scholar
[4]Rangaswamy, K.M. and Vanaja, N., “Quasi-projectives and their generalisations”, (to appear).Google Scholar
[5]Utumi, Y., “On continuous regular rings”, Canad. Math. Bull. 4 (1961), 63–69.CrossRefGoogle Scholar