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Proceedings of the American Mathematical Society

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

 

 

Frobenius extensions of QF-$ 3$ rings


Author: Yoshimi Kitamura
Journal: Proc. Amer. Math. Soc. 79 (1980), 527-532
MSC: Primary 16A36; Secondary 16A56
DOI: https://doi.org/10.1090/S0002-9939-1980-0572295-2
MathSciNet review: 572295
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Abstract: We investigate the inheritance of QF-3 property for ring extensions, mainly, for Frobenius extensions. Let A be a ring with identity. It is proved that a group ring $ A[G]$ of A with a finite group G is left QF-3 iff A is left QF-3 and that in case A is a. G-Galois extension of the fixed subring $ {A^G}$ relative to a finite group G of ring automorphism of A, A is left QF-3 iff $ {A^G}$ is left QF-3.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0572295-2
Keywords: Frobenius extensions, QF-3 rings, group rings, G-Galois extensions, Quasi-Frobenius extensions, minimal faithful modules, cofinitely generated modules, trivial crossed products
Article copyright: © Copyright 1980 American Mathematical Society