Fraction-Dense Algebras and Spaces

A. W. Hager and Jorge Martinez
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A. W. Hager: Wesleyan University, Department of Mathematics
Jorge Martinez: University of Florida, Department of Mathematics

A chapter in Positive Operators and Semigroups on Banach Lattices, 1992, pp 55-65 from Springer

Abstract: Abstract 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 fraction-dense f-rings are characterized as those for which the space of minimal prime ideals is compact and externally disconnected. For Archimedean lattice-ordered groups with this property it is shown that the Dedekind and order completion coincide. Fraction-dense 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.

Keywords: commutative ring; fraction-dense ring; fraction dense space (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-94-017-2721-1_6

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