Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T14:44:24.130Z Has data issue: false hasContentIssue false
  • English
  • Français

Induced and Produced Modules

Published online by Cambridge University Press:  20 November 2018

D. G. Higman
D. G. Higman*
Affiliation:
Montana State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We shall consider here two generalizations to rings of the concept of induced representation as it occurs in the representation theory of finite groups (6).

If A is a ring, S a subring of A, we shall associate with each S-module M an induced pair (I(M), K) consisting of an A -modulo I(M) and an S-homomorphism K: M → I(M).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 490 - 508
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Baer, R., Abelian groups that are direct summands of every containing abetian group, Bull. Amer. Math. Soc, 46 (1940), 800–806.Google Scholar
2. Eckmann, B., On complexes with operators, Proc. Nat. Acad. Science, 89 (1953), 35–42.Google Scholar
3. Eckmann, B., Cohomology of groups and transfer, Ann. of Math., 58 (1953), 481–493.Google Scholar
4. Eckmann, B. and Schopf, A., Über injektive Moduln, Archiv der Mathematik, 4 (1953), 75–78.Google Scholar
5. Gaschiitz, W., Über den Fundamentalsatz von Maschke zur Darstellungstheorie der endlichen Gruppen, Math., Z., 56 (1952), 376–387.Google Scholar
6. Frobenius, G., Über Rehationen zivischen den Character en einen Gruppe und denen ihrer Untergruppen, S.-B. preuss. Akad. Wiss., 1898, 501–515.Google Scholar
7. Higman, D. G., On modules with a group of operators, Duke Math. J., 21 (1954), 369–376.Google Scholar
8. Higman, D. G., Indecomposable representations of characteristic p, Duke Math. J., 21 (1954), 377–382.Google Scholar
9. Hochschild, G., Semi-simple algebras and generalized derivations, Amer. J. Math., 64 (1941), 677–694.Google Scholar
10. Hochschild, G., On the cohomology theory for associative algebras, Ann. Math., 47 (1946), 568–579.Google Scholar
11. Levitski, J., Eine neue Anwendreng der Darstellung einen endlichen Gruppe als monomiale Matrizengruppe, Math. Z., 88 (1934), 301–305.Google Scholar
12. MacLane, S., Duality for groups, Bull. Amer. Math. Soc, 56 (1950), 485–516.Google Scholar
13. Nakayama, T., On Frobenius algebras I, Ann. Math., 40 (1939), 611–633.Google Scholar
14. Nakayama, T., On Frobenius algebras, II, Ann. Math., 42 (1941), 1–21.Google Scholar
15. Zassenhaus, H., Induced representations, unpublished.Google Scholar