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A note on quasi-Frobenius rings


Authors: Dinh Van Huynh and Ngo Si Tung
Journal: Proc. Amer. Math. Soc. 124 (1996), 371-375
MSC (1991): Primary 16L60, 16D50
MathSciNet review: 1322929
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Abstract: It is shown that a semiperfect ring $R$ is quasi-Frobenius if and only if every closed submodule of $R(\omega )$ is non-small, where $R(\omega )$ denotes the direct sum of $\omega $ copies of the right $R$-module $R$ and $\omega $ is the first infinite ordinal.


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Additional Information

Dinh Van Huynh
Affiliation: Institute of Mathematics, P. O. Box 631 Boho, Hanoi, Vietnam

Ngo Si Tung
Affiliation: Institute of Mathematics, P. O. Box 631 Boho, Hanoi, Vietnam
Email: huynh@math.ohio-state.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03303-5
Keywords: Closed submodules, small modules, non-small modules, quasi-\linebreak Frobenius rings
Received by editor(s): August 22, 1994
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society