Representation of abelian groups and rings by families of real-valued functions
Author: Carl W. Kohls
Journal: Proc. Amer. Math. Soc. 25 (1970), 86-92
MSC: Primary 06.78; Secondary 46.00
MathSciNet review: 0256964
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Abstract: Sufficient conditions are indicated for the existence of an isomorphism of an abelian group or ring into the family of real-valued continuous functions on a realcompact or compact space. The spaces consist of sets of subsemigroups or subsemirings that are maximal among those containing a fixed element but not containing its additive inverse; in the ring case, where the element is the multiplicative identity, these are just infinite primes in the sense of Harrison. Earlier results of Harrison, Kadison, and Krivine follow from the present discussion.
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Keywords: Ordered abelian group, ordered vector space, ordered ring, ordered algebra, Archimedean totally ordered group, representation, real-valued continuous function, realcompact space, compact space, Harrison infinite prime, extreme point
Article copyright: © Copyright 1970 American Mathematical Society