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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commutative perfect $ {\rm QF}-1$ rings


Author: Hiroyuki Tachikawa
Journal: Proc. Amer. Math. Soc. 68 (1978), 261-264
MSC: Primary 16A36
MathSciNet review: 0472903
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Abstract: If R is a commutative artinian ring, then it is known that every finitely generated faithful R-module is balanced (i.e. has the double centralizer property) if and only if R is a quasi-Frobenius ring. In this note, constructing new nonbalanced modules we prove that the assumption on R to be artinian can be replaced by the weaker condition that R is perfect.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0472903-1
PII: S 0002-9939(1978)0472903-1
Keywords: QF-1 ring, quasi-Frobenius ring, perfect ring, injective cogenerator, balanced module
Article copyright: © Copyright 1978 American Mathematical Society