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On the equivalence of integral representations of groups


Author: A. Białynicki-Birula
Journal: Proc. Amer. Math. Soc. 26 (1970), 371-377
MSC: Primary 20.80; Secondary 16.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0268291-9
MathSciNet review: 0268291
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Abstract: Let $ R$ be a local ring and let $ R'$ be a commutative $ R$-algebra faithfully flat as an $ R$-module. Let $ G$ be a finitely generated group and let $ M,N$ be $ RG$-modules, finitely presented over $ R$. Let $ M' = M{ \otimes _R}R';N' = N{ \otimes _R}R'$, then $ M',N'$ can be considered as $ R'G$-modules. We shall prove that the $ R'G$-modules $ M',N'$ are isomorphic if and only if the $ RG$-modules $ M$ and $ N$ are isomorphic. The proof depends on a theorem on noncommutative cohomology which is presented in the first part of the paper.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0268291-9
Keywords: Algebras over local rings, representations of algebras, integral representations of groups, faithfully flat commutative algebras, noncommutative Amitsur cohomology
Article copyright: © Copyright 1970 American Mathematical Society

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