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Positive Operators and Semigroups on Banach Lattices pp 55–65Cite as

Fraction-Dense Algebras and Spaces

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Wesleyan University, Middletown, CT, 06457, USA

    A. W. Hager

  2. Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    Jorge Martinez

Authors
  1. A. W. Hager
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  2. Jorge Martinez
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Leiden University, Leiden, The Netherlands

    C. B. Huijsmans

  2. California Institute of Technology, Pasadena, USA

    W. A. J. Luxemburg

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© 1992 Springer Science+Business Media Dordrecht

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Hager, A.W., Martinez, J. (1992). Fraction-Dense Algebras and Spaces. In: Huijsmans, C.B., Luxemburg, W.A.J. (eds) Positive Operators and Semigroups on Banach Lattices. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2721-1_6

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  • DOI: https://doi.org/10.1007/978-94-017-2721-1_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4205-7

  • Online ISBN: 978-94-017-2721-1

  • eBook Packages: Springer Book Archive

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