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Proceedings of the American Mathematical Society

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

 

 

A characterization of Steinitz group rings


Authors: Paul J. Allen and Joseph Neggers
Journal: Proc. Amer. Math. Soc. 49 (1975), 39-42
DOI: https://doi.org/10.1090/S0002-9939-1975-0360668-0
MathSciNet review: 0360668
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Abstract | References | Additional Information

Abstract: A ring $ R$ with an identity is a (right) Steinitz ring provided any linearly independent subset of a free (right) $ R$-module can be extended to a basis for the module by adjoining elements from any given basis. In this paper, we characterize those group rings which are Steinitz rings by the following:

Theorem. The group ring $ R[G]$ is a Steinitz ring if and only if $ R$ is a Steinitz ring and either (1) char $ R = {p^i}$ and $ G$ is a finite $ p$-group or (2) char $ R = 0$ and $ G = 1$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0360668-0
Keywords: Group ring, Steinitz ring, $ T$-nilpotent Jacobson radical
Article copyright: © Copyright 1975 American Mathematical Society