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On Commuting Rings Of Endomorphisms

Published online by Cambridge University Press:  20 November 2018

C. W. Curtis*
Affiliation:
University of Wisconsin
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Various problems concerning the general theory of centralizers of modules which are not assumed to be completely reducible have been discussed by Fitting (3), Brauer (2), and Nakayama. In this paper we present a new approach to some of these questions, which has its origin in Weyl's discussion (15) of the centralizer of a finite group of collineations.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Artin, E., Nesbitt, C. J., and Thrall, R. M., Rings with minimum condition, University of Michigan Publications in Mathematics, No. 1, 1944.Google Scholar
2. Brauer, R., On sets of matrices with coefficients in a division ring, Trans. Amer. Math. Soc, 49 (1951), 502548.Google Scholar
3. Fitting, H., Die Theorie der Automorphismenringe Abels cher Gruppen und ihr Analogen bei nicht kommutativen Gruppen, Math. Ann., 107 (1932), 514542.Google Scholar
4. Gaschütz, W., Über der Fundamentalsatz von Maschke zur Darstellungstheorie der endlichen Gruppen, Math. Z., 56 (1952), 376387.Google Scholar
5. Kasch, F., Grundlagen einer Theorie der Frobeniuserweiterungen, Math. Ann., 127 (1954), 453474.Google Scholar
6. Jacobson, N., The theory of rings, Mathematical Surveys, II (New York, 1943).Google Scholar
7. Jacobson, N., The radical and semi-simplicity for arbitrary rings, Amer. J. Math., 67 (1945), 300320.Google Scholar
8. Jacobson, N., Lectures in abstract algebra, II (New York, 1953).Google Scholar
9. Nagao, H. and Nakayama, T., On the structure of (Mo) and (Mu) modules, Math. Zeit, 59 (1953), 164170.Google Scholar
10. Nakayama, T., On Frobeniusean algebras, I, Ann. Math., 40 (1939), 611633.Google Scholar
11. Nakayama, T., On Frobeniusean algebras II, Ann. Math., 42 (1941), 121.Google Scholar
12. Nesbitt, C., On the regular representations of algebras, Ann. Math., 39 (1938), 634658.Google Scholar
13. Nesbitt, C. and Thrall, R., Some ring theorems with applications to modular representations, Ann. Math., 47 (1946), 551567.Google Scholar
14. Thrall, R., Some generalizations of quasi-Frobenius algebras, Trans. Amer. Math. Soc, 64 (1948), 173183.Google Scholar
15. Weyl, H., Commutator algebra of a finite group of collineations, Duke Math. J., 3 (1937), 200212.Google Scholar
16. Weyl, H., The theory of groups and quantum mechanics (New York, 1931).Google Scholar
17. Weyl, H., The classical groups (Princeton, 1939).Google Scholar