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Note on a Subring of C*(X)(1)

Published online by Cambridge University Press:  20 November 2018

Choo Eng-Ung
Choo Eng-Ung*
Affiliation:
University of Science of Malaysia, Penang, Malaysia
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Throughout, topological spaces are assumed to be completely regular. C(X) (resp. C*(X)) will denote the ring of all (resp. all bounded) continuous real-valued functions. βX will denote the Stone-Cech compactification of X. In [2], Nel and Riorden defined C≠(X) to be the set of all f ∊ C(X) such that M(f) is real in the residue class ring C(X)/M for every maximal ideal M in C(X). C≠(X) is a subalgebra as well as a sublattice of C*(X).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 177 - 179
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

(1)

This paper is a part of the author's Ph.D. thesis at the University of British Columbia written under the supervision of J. V. Whittaker.

References

1. Gillman, L. and Jerison, M., Rings of Continuous Functions, Van Nostrand, N.Y., 1960.Google Scholar
2. Nel, L. D. and Riordan, D., Note on a Subalgebra of C(X), Cand. Math. Bull. Vol. 15 (4), 1972.Google Scholar