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On strongly right bounded finite rings

Published online by Cambridge University Press:  17 April 2009

Weimin Xue
Weimin Xue
Affiliation:
Department of Mathematics Fujian Normal, University Fuzhou Fujian, 350007 Peoples, Republic of China
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Abstract

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An associative ring is called strongly right (left) bounded if every nonzero right (left) ideal contains a nonzero ideal. We prove that if R is a strongly right bounded finite ring with unity and the order |R| of R has no factors of the form p5, then R is strongly left bounded. This answers a question of Birkenmeier and Tucci.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 353 - 355
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Birkenmeier, G.F. and Tucci, R.P., ‘Homomorphic images and the singular ideal of a strongly right bounded ring’, Comm. Algebra 16 (1988), 1099–1112, 2661–2662.CrossRefGoogle Scholar
[2]Courier, R.C., ‘Finite dimensional right duo algebras are duo’, Proc. Amer. Math. Soc. 84 (1982), 157–161.Google Scholar
[3]Eldridge, K.E., ‘Orders for finite noncommutative rings with unity’, Amer. Math. Monthly 75 (1968), 512–514.CrossRefGoogle Scholar