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On Utumi's Ring of Quotients

Published online by Cambridge University Press:  20 November 2018

Joachim Lambek
Joachim Lambek*
Affiliation:
McGill University
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The purpose of this note is to establish and exploit the fact that Utumi's maximal ring of right quotients (6) of an associative ring R (let us say with 1) is the bicommutator of the minimal injective extension of R regarded as a right R-module. Nothing new will be said about Johnson's ring of quotients (4), which is still the most important case.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 363 - 370
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Bourbaki, N., Eléments de mathématique, Vol. 23 (Paris, 1958), and Vol. 27 (Paris, 1961).Google Scholar
2. Eckmann, B. and Schopf, A., Über injektive Moduln, Arch. Math., 4 (1956), 75–78.Google Scholar
3. Findlay, G. D. and Lambek, J., A generalized ring of quotients, Can. Math. Bull., 1 (1958), 77–85, 155-167.Google Scholar
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5. Johnson, R. E., Quotient rings of rings with zero singular ideal, Pacific J. Math., 11 (1961), 1385– 1395.Google Scholar
6. Utumi, Y., On quotient rings, Osaka Math. J., 8 (1956), 1–18.Google Scholar
7. Utumi, Y., On a theorem on modular lattices, Proc. Japan Acad., 35 (1959), 16–21.Google Scholar
8. Wong, E. T. and Johnson, R. E., Self-infective rings, Can. Math. Bull., 2 (1959), 167–174.Google Scholar