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Integral Representations of the Direct Product of Groups

Published online by Cambridge University Press:  20 November 2018

Alfredo Jones
Alfredo Jones*
Affiliation:
University of Illinois
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Let G be a finite group and R a Dedekind domain with quotient field K. We denote by RG the group ring of formal linear combinations of elements of G with coefficients in R. By an RG-module we understand a unital left RG-module which is finitely generated and torsion-free as R-module. In particular, if R is a principal ideal domain this is equivalent to considering representations of G by matrices with entries in R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 625 - 630
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Cartan, H. and Eilenberg, S., Homological algebra (Princeton, 1956).Google Scholar
2. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (New York, 1962).Google Scholar
3. Heller, A., On group representations over a valuation ringt Proc. Natl. Acad. Sci. U.S., 47 (1961), 1194–1197.Google Scholar
4. Maranda, J. M., On the equivalence of representations of finite groups by groups of automorphisms of modules over Dedekind rings, Can. J. Math., 7 (1955), 516–526.Google Scholar