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Special Subrings of Real, Continuous Functions

出版	University of Missouri--Rolla, 1971
URL	http://books.google.com.hk/books?id=syzqNwAACAAJ&hl=&source=gbs_api

註釋"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 [beta]x is associated with a lattice-ordered subring of C(X) which is isomorphic to C(Y) and contains C*(X). The cardinal number of ([Beta]X - [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 C[subscript K[(X), the continuous functions of compact support, and C[subscript infinity] (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, leaf ii