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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Commutative $ {\rm QF}-1$ artinian rings are $ {\rm QF}$

Authors: S. E. Dickson and K. R. Fuller
Journal: Proc. Amer. Math. Soc. 24 (1970), 667-670
MSC: Primary 16.25
MathSciNet review: 0252426
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Abstract: In a recent paper, D. R. Floyd proved several results on algebras, each of whose faithful representations is its own bicommutant ( = R. M. Thrall's $ {\text{QF - }}1$ algebras, a generalization of $ {\text{QF}}$-algebras) among which was the theorem in the title for algebras. We obtain our extension of Floyd's result by use of interlacing modules, replacing his arguments involving the representations themselves.

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Keywords: $ {\text{QF - }}1$ ring, $ {\text{QF}}$-ring, Frobenius ring, quasi-Frobenius ring, artinian ring, faithful module, bicommutant, double centralizer property
Article copyright: © Copyright 1970 American Mathematical Society