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

DOI:
https://doi.org/10.1090/S0002-9939-96-03303-5

MathSciNet review:
1322929

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Abstract | References | Similar Articles | Additional Information

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

Keywords:
Closed submodules,
small modules,
non-small modules,
quasi- Frobenius rings

Received by editor(s):
August 22, 1994

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1996
American Mathematical Society