Doctoral Dissertations

Abstract

"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.

Advisor(s)

Pursell, Lyle E.

Committee Member(s)

Hicks, Troy L.
Jones, R. E. Douglas
Ho, C. Y. (Chung You), 1933-1988
Rivers, Jack L.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

1971

Pagination

iv, 124 pages

Note about bibliography

Includes bibliographical references (pages 120-121).

Rights

© 1971 Paul Marlin Harms, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Library of Congress Subject Headings

Functions, Continuous
Rings (Algebra)
Functional analysis
Analytic functions

Thesis Number

T 2615

Print OCLC #

6038272

Electronic OCLC #

874750881

Included in

Mathematics Commons

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