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Remarks on Rings of Quotients of Rings of Functions

Published online by Cambridge University Press:  20 November 2018

Harry Gonshor
Harry Gonshor*
Affiliation:
Rutgers University, New Brunswick, New Jersey
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This paper was inspired by [4]. The main result there suggests a close relationship between injective hulls of C* algebras as studied in [2] and [3] and rational completions as studied in [1]. We shall prove an analogue of Theorem 1 in [3] for rational completions. The latter theorem states that the injective hull of the algebra C(X) of all complex valued functions on the compact Hausdorff space X is the algebra B(X) of all bounded Borel functions modulo sets of first category.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 159 - 160
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Fine, N., Gillman, L., and Lambek, J., Rings of quotients of rings of fund ions, McGill Univ. Press, Montreal, 1965.Google Scholar
2. Gonshor, H., Injective hulls ofC* algebras, Trans. Amer. Math. Soc. 131 (1968), 315-322.Google Scholar
3. Gonshor, H., Injective hulls of C* algebras II, Proc. Amer. Math. Soc. 24 (1970), 486-491.Google Scholar
4. Park, Y.L., On the projective cover of the Stone-Cech compactification of a completely regular Hausdorff space, Canad. Math. Bull. 12 (1969), 327-331.Google Scholar