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Some characterizations of π-regular rings with no infinite trivial subring

Published online by Cambridge University Press:  20 January 2009

Yasuyuki Hirano
Yasuyuki Hirano
Affiliation:
Department of MathematicsOkayama UniversityOkayama 700, Japan
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Abstract

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It is shown that a ring R is a π-regular ring with no infinite trivial subring if and only if R is a subdirect sum of a strongly regular ring and a finite ring. Some other characterizations of such a ring are given. Similar result is proved for a periodic ring. As a corollary, it is shown that every δ-ring is a subdirect sum of a Unite ring and a commutative ring. This was conjectured by Putcha and Yaqub.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 1 , February 1991 , pp. 1 - 5
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Armendariz, E. P.On infinite periodic rings, Math. Scand. 59 (1986), 5–8.CrossRefGoogle Scholar
2.Azumaya, G.Strongly π-regular rings, J. Fac. Sci. Hokkaido Univ. 13 (1954), 34–39.Google Scholar
3.Chacron, M., On a theorem of Herstein, Canad. J. Math. 21 (1969), 1348–1353.CrossRefGoogle Scholar
4.Fisher, J. W. and Snider, R. L.On the von Neumann regularity of rings with regular prime factor rings, Pacific J. Math. 54 (1974), 135–144.CrossRefGoogle Scholar
5.Herstein, I. N.Noncommutative Rings (Carus Monogr. No. 15, Amer. Math. Ass., New York, 1968).Google Scholar
6.Hirano, Y., On π-regular rings with no infinite trivial subring, Math. Scand., to appear.Google Scholar
7.Laffey, T. J.Commutative subrings of periodic rings, Math. Scand. 39 (1976), 161–166.CrossRefGoogle Scholar
8.Putcha, M. S. and Yaqub, A., A finiteness conditions for rings, Math. Japan. 22 (1977), 13–20.Google Scholar