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A Note on Induced Modules

Published online by Cambridge University Press:  20 November 2018

Charles W. Curtis
Charles W. Curtis*
Affiliation:
University of Wisconsin
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In this paper, A denotes a ring with an identity element 1, and B a subring of A containing 1 such that B satisfies the left and right minimum conditions, and A is a finitely generated left and right B-module. The identity element 1 is required to act as the identity operator on all modules which we shall consider. For any left B-module V, there is a standard construction of a left A -module which is, roughly speaking, the smallest A -module containing V.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 587 - 592
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Eilenberg, S. and Nakayama, T., On the dimension of modules and algebras II, Nagoya Math. J., 9 (1955), 1–16.Google Scholar
2. Higman, D. G., Indecomposable representations at characteristic p, Duke Math. J., 21 (1954), 377–381.Google Scholar
3. Higman, D. G., Induced and produced modules, Can. J. Math., 7 (1955), 490–508.Google Scholar
4. Higman, D. G., Relative cohomology, Can. J. Math., 9 (1957), 19–34.Google Scholar
5. Hochschild, G., Relative homologuai algebra, Trans. Amer. Math. Soc, 82 (1956), 246–269.Google Scholar
6. Jans, J. P., On the indecomposable representations of algebras, Ann. of Math., 66 (1957), 418–429.Google Scholar
7. Nagao, H. and Nakayama, T., On the structure of the (Mo) and (Mu)-modules, Math. Zeit., 59 (1953), 164–170.Google Scholar
8. Nesbitt, C. and Thrall, R., Some ring theorems with applications to modular representations, Ann. of Math., 47 (1946), 551–567.Google Scholar