"Some lattice-ordered subrings of C(X) containing C*(X) are examined where X is a completely regular space. Each realcompact spaceY between [v]x and ßx is associated with a lattice-ordered subring of C(X) which is isomorphic to C(Y) and contains C*(X). The cardinal number of (ßX - [v]X) is a lower bound for the cardinal number of these subrings. Every prime ideal in each of these subrings is comparable with the intersection of the subring and a maximal ideal in C(X). The structure space of maximal ideals is studied for special subrings in C(X) containing CK(X), the continuous functions of compact support, and C∞ (X), the continuous functions converging to 0 at infinity. Examples of structure spaces are given which are homeomorphic to finite point compactifications of R"--Abstract, page ii.
Pursell, Lyle E.
Hicks, Troy L.
Jones, R. E. Douglas
Ho, C. Y. (Chung You), 1933-1988
Rivers, Jack L.
Mathematics and Statistics
Ph. D. in Mathematics
University of Missouri--Rolla
iv, 124 pages
© 1971 Paul Marlin Harms, All rights reserved.
Dissertation - Open Access
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Link to Catalog Recordhttp://laurel.lso.missouri.edu/record=b1066393~S5
Harms, Paul Marlin, "Special subrings of real, continuous functions" (1971). Doctoral Dissertations. 2269.