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Fraction-Dense Algebras and Spaces

Published online by Cambridge University Press:  20 November 2018

Anthony W. Hager  and
Jorge Martinez
Anthony W. Hager
Affiliation:
Department of Mathematics Wesleyan University Middletown, Connecticut 06457 U.S.A.
Jorge Martinez
Affiliation:
Department of Mathematics University of Florida Gainesville, Florida 32611 U.S.A.
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Abstract

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A fraction-dense (semi-prime) commutative ring A with 1 is one for which the classical quotient ring is rigid in its maximal quotient ring. The fractiondense ƒ- rings are characterized as those for which the space of minimal prime ideals is compact and extremally disconnected. For archimedean lattice-ordered groups with this property it is shown that the Dedekind and order completion coincide. Fractiondense spaces are defined as those for which C(X) is fraction-dense. If X is compact, then this notion is equivalent to the coincidence of the absolute of X and its quasi-F cover. R-embeddings of Tychonoff spaces are re-introduced and examined in the context of fraction-density.

Keywords

06F2554C40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 977 - 996
Copyright
Copyright © Canadian Mathematical Society 1993

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