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Proceedings of the American Mathematical Society

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

 

 

Balanced and $ QF-1$ algebras


Authors: V. P. Camillo and K. R. Fuller
Journal: Proc. Amer. Math. Soc. 34 (1972), 373-378
MSC: Primary 16A36
DOI: https://doi.org/10.1090/S0002-9939-1972-0306256-0
MathSciNet review: 0306256
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Abstract: A ring R is QF-1 if every faithful module has the double centralizer property. It is proved that a local finite dimensional algebra is QF-1 if and only if it is QF. From this it follows that an arbitrary finite dimensional algebra has the property that every homomorphic image is QF-1 if and only if every homomorphic image is QF.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0306256-0
Keywords: Quasi-Frobenius, QF-1, finite dimensional algebra, double centralizer
Article copyright: © Copyright 1972 American Mathematical Society