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On Maximal Rings of Right Quotients

Published online by Cambridge University Press:  20 November 2018

Joanne Christensen
Joanne Christensen*
Affiliation:
Hamilton College McMaster University
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Utumi has shown [3, Claim 5.1] that for a certain class of rings the associated maximal rings of right quotients are isomorphic to the endomorphism rings of modules over division rings. We shall prove a generalization of this theorem and then show how it is obtained as a corollary. The following proofs do not depend on Utumi's paper; instead, they make extensive use of results proved in [1]. The terminology and notations employed here are the same as in [1].

I wish to thank Dr. B. Banaschewski for his suggestions and helpful criticism.

LEMMA: If J is a left ideal with zero left annihilator in a ring R then a maximal ring of right quotients of R is also a maximal ring of right quotients of J.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 2 , May 1962 , pp. 147 - 149
Copyright
Copyright © Canadian Mathematical Society 1962

References

1. Findlay, G. D. and Lambek, J., A generalized ring of quotients I, II, Can. Math. Bull., 1 (1958), 77-85, 155-167.10.4153/CMB-1958-016-6Google Scholar
2. Lambek, J., On the structure of semi-prime rings and their rings of quotients, Can. Math. Bull., 13 (1961), 392-417.10.4153/CJM-1961-033-1Google Scholar
3. Utumi, Y., On quotient rings, Osaka Math. J., 8 (1956), 1-18.Google Scholar