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On Quotient-Like Extensions of C(X)

Published online by Cambridge University Press:  20 November 2018

Young L. Park
Young L. Park*
Affiliation:
McMaster University
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The maximal ring of quotients (in the sense of Johnson [4] and Utumi [5[) of the ring C(X) of real valued continuous functions on a completely regular Hausdorff space X has been studied in [1] and [2]. The aim of the present paper is to provide some additional results to those, and to study the relevant extensions on the absence of the real maximal ideals.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 6 , December 1969 , pp. 793 - 799
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Banaschewski, B., Maximal rings of quotients of semisimple commutative rings. Arch. Math. 16 (1965) 414–420.Google Scholar
2. Fine, N., Gillman, L. and Lambek, J., Rings of quotients of rings of functions. (McGill Univ. Press, Montreal, 1965.)Google Scholar
3. Gillman, L. and Jerison, M., Rings of continuous functions. (Princeton, 1960.)Google Scholar
4. Johnson, R., The extended centralizer of a ring over a module. Proc. Amer. Math. Soc. 2 (1951) 891–895.Google Scholar
5. Utumi, Y., On quotient rings. Osaka Math. J. 8 (1956) 1–18.Google Scholar