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On Utumi's Ring of Quotients

  • Joachim Lambek (a1)

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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.

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References

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1. Bourbaki, N., Eléments de mathématique, Vol. 23 (Paris, 1958), and Vol. 27 (Paris, 1961).
2. Eckmann, B. and Schopf, A., Über injektive Moduln, Arch. Math., 4 (1956), 7578.
3. Findlay, G. D. and Lambek, J., A generalized ring of quotients, Can. Math. Bull., 1 (1958), 7785, 155-167.
4. Johnson, R. E., The extended centralizer of a ring over a module, Proc. Amer. Math. Soc, 2 (1951), 891895.
5. Johnson, R. E., Quotient rings of rings with zero singular ideal, Pacific J. Math., 11 (1961), 1385 1395.
6. Utumi, Y., On quotient rings, Osaka Math. J., 8 (1956), 118.
7. Utumi, Y., On a theorem on modular lattices, Proc. Japan Acad., 35 (1959), 1621.
8. Wong, E. T. and Johnson, R. E., Self-infective rings, Can. Math. Bull., 2 (1959), 167174.
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On Utumi's Ring of Quotients

  • Joachim Lambek (a1)

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