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Ring Theoretic Properties of Matrix Rings

Published online by Cambridge University Press:  20 November 2018

S.M. Kaye
S.M. Kaye*
Affiliation:
McGill University
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K. Morita has shown that, given two rings R and S, there is an isomorphism between the category of left R-modules and the category of left S-modules if and only if there exists an R-S bimodule U such that

(1) U is a progenerator in the category of left R-modules, and

(2) S ≅ (EndR U)opp as rings.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 365 - 374
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Bass, H., Finitistic Dimension and a Homological Generalization of Semi - primary Rings. Trans. Am. Math. Soc. vol. 95 (June, 1960), 466-488.Google Scholar
2. Bass, H., The Morita Theorems. University of Oregon lecture notes (1966).Google Scholar
3. Cartan, H. and Eilenberg, S., Homo logical Algebra. Princeton University Press (1955).Google Scholar
4. Lambek, J., Lectures on Rings and Modules. Blaisdell (1966).Google Scholar
5. Levy, L., Torsion-free and Divisible Modules over Non-Integral-Domains. Can. Jour. Math.. Vol. 15, No. l (1966) 132-151.Google Scholar
6. Morita, K., Duality Theorems for Modules and its Application to the Theory of Rings with Minimum Condition. Sc. Rep. Tokyo KyoikuDaigaku. vol. 6 (1955), 83-142.Google Scholar
7. Utumi, Y., On Continuous Rings and Self-injective Rings. Trans. Am. Math. Soc. vol. 118 (June, 1965), 158-173.Google Scholar