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On the Group Ring

Published online by Cambridge University Press:  20 November 2018

Ian G. Connell
Ian G. Connell*
Affiliation:
McGill University, Montreal, Quebec
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Let R be the discrete group ring of the group G over the ring A. In this paper we attempt to find necessary and sufficient conditions on G and A so that R will have some standard ring-theoretic property ; among the properties considered are those of being artinian, regular, self-injective, and semi-prime.

The contents of this paper form essentially the author's doctoral thesis. The author would like to thank his supervisor Dr. J. Lambek for his generous encouragement and continued interest.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 650 - 685
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Amitsur, S. A., On the semi-simplicity of group algebras, Mich. Math. J., 6 (1959), 251–253.Google Scholar
2. Auslander, M., On regular group rings, Proc. Amer. Math. Soc, 8 (1957), 658–664.Google Scholar
3. Birkhoff, G., Lattice theory , rev. ed. (Providence, 1948).Google Scholar
4. Bourbaki, N., Algèbre, chap. 8 (Paris, 1958).Google Scholar
5. Cartan, H. and Eilenberg, S., Homologuai algebra (Princeton, 1956).Google Scholar
6. Deskins, W. E., Finite abelian groups with isomorphic group algebras, Duke Math. J., 23 (1956), 35–40.Google Scholar
7. Eilenberg, S. and Nakayama, T., On the dimension of modules and algebras II, Nagoya Math. J., 9 (1955), 1–16.Google Scholar
8. Jacobson, N., Lectures in abstract algebra, vol. 1 (Princeton, 1951).Google Scholar
9. Jacobson, N., Structure of rings (Providence, 1956).Google Scholar
10. Jennings, S. A., The structure of the group ring of a p-group over a modular field, Trans. Amer. Math. Soc, 50 (1941), 175–185.Google Scholar
11. Jennings, S. A., The group ring of a class of infinite nilpotent groups, Can. J. Math., 7 (1955), 169– 187.Google Scholar
12. Kaplansky, I., Report of a conference on linear algebras, publ. 502, (Arner.) Nat. Acad. Sci., National Research Council (1957).Google Scholar
13. Losey, G., On dimension subgroups, Trans. Amer. Math. Soc, 97 (1960), 474–486.Google Scholar
14. Losey, G., On group algebras of p-group s, Mich. Math. J., 7 (1960), 237–240.Google Scholar
15. McCoy, N. H., Rings and ideals (New York, 1948).Google Scholar
16. McLaughlin, J. E., A note on regular group rings, Mich. Math. J., 5 (1958), 127–128.Google Scholar
17. Passman, D. S., Nil ideals in group rings, Mich. Math. J., 9 (1962), 375–384.Google Scholar
18. Suzuki, M., Structure of a group and the structure of its lattice of subgroups (Berlin, 1956).Google Scholar
19. Villamayor, O. E., On the semi-simplicity of group algebras, Proc Amer. Math. Soc, 9 (1958), 621–627.Google Scholar
20. Villamayor, O. E., On the semi-simplicity of group algebras, II, Proc. Amer. Math. Soc, 10 (1959), 27–31.Google Scholar
21. Neumann, B. H., Groups with finite classes of conjugate elements, Proc. London Math. Soc, 1 (1951), 178–187.Google Scholar
22. Kurosh, A. G., Theory of groups, translated by K. A. Hirsch, vol. 2 (New York, 1960). Google Scholar