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A Type of Quasi-Frobenius Ring

Published online by Cambridge University Press:  20 November 2018

Edmund H. Feller
Edmund H. Feller*
Affiliation:
University of Wisconsin-Milwaukee
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In [3], the author proved that a ring R with identity is right noetherian and right injective if and only if R is a direct sum of a finite number of uniform right ideals, which are completely primary in the sense of that paper. In this paper, we shall determine the structure of such rings in the case where the sum of the isomorphic uniform components are twosided ideals. The ring is found to be a direct sum of total matrix rings over local rings.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 19 - 27
Copyright
Copyright © Canadian Mathematical Society 1967

Footnotes

1

Research supported by the N. S.F. under grant GP - 4453.

References

1. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras. Interscience Pubhl. (1966).Google Scholar
2. Feller, E. H., The lattice of submodules of a module over a noncommutative ring. Trans. Amer. Math. Soc. 81 (1955) pages 342-357.CrossRefGoogle Scholar
3. Feller, E. H., Noetherian modules and noetherian injective rings. Tohoku Math. Jr.. vol. 17 (1966), pages 130-138.Google Scholar
4. Goldie, A. W., Semi-prime rings with maximum condition. Proc. London Math. Soc, 8 (1955), pages 589-608.Google Scholar
5. Her stein, I. N., Topics in ring theory. Math lecture notes, U. of Chicago (1966).Google Scholar
6. Jacobson, N., Structure of rings. Amer. Math. Soc. Colloq. Publ. vol. 37 (1955).Google Scholar
7. Lambek, J., On the ring of quotients of a noetherian ring. Canad. Math. Bull. vol. 8, no, 3, April (1966), pages 279-290.CrossRefGoogle Scholar
8. Morita, K., Duality for modules and its applications to the theory of rings with minimum conditions. Science reports of the Tokya Kyoiku Daigaku, Vol. 6. No. 150 (1955), pages 83-142.Google Scholar
9. Nakayama, T., On Frobenius algebras I. Ann. o. Math. 40 (1933), pages 611-633.Google Scholar
10. Levy, L., Torsion free and divisible modules over nonintegral domains. Canad. Jr. of Math. vol. 15 (1966), pages 132-151.Google Scholar