A characterization of Steinitz group rings
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- by Paul J. Allen and Joseph Neggers PDF
- Proc. Amer. Math. Soc. 49 (1975), 39-42 Request permission
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 $G = 1$.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 39-42
- DOI: https://doi.org/10.1090/S0002-9939-1975-0360668-0
- MathSciNet review: 0360668