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An approach to Boyle's conjecture

Published online by Cambridge University Press:  20 January 2009

Dinh van Huynh  and
S. Tariq Rizvi
Dinh van Huynh
Affiliation:
Institute of Mathematics, P.O. Box 631 Boho, Hanoi, Vietnam
S. Tariq Rizvi
Affiliation:
The Ohio State University at Lima, Lima, OH 45804, U.S.A.
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Abstract

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A ring R is called a right QI-ring if every quasi-injective right R-module is injective. The well-known Boyle's Conjecture states that any right QI-ring is right hereditary. In this paper we show that if every continuous right module over a ring R is injective, then R is semisimple artinian. In fact, if every singular continuous right R-module satisfying the restricted semisimple condition is injective, then R is right hereditary. Moreover, in this case, every singular right R-module is injective.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 2 , June 1997 , pp. 267 - 273
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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