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Reflections on the Global Dimensions of Rings of Continuous Functions

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Ordered Algebraic Structures

Abstract

In the mid 1950s the theory of rings of continuous functions began a rapid development, most notably with the publication of Gillman and Henriksen’s two papers Concerning rings of continuous functions and Rings of continuous functions in which every finitely generated ideal is principal. These papers (which characterized von Neumann regular rings and Bézout rings of real valued continuous functions, respectively) can be seen as the beginning of a theory of rings of continuous functions, whose aim was to investigate the interaction between topological properties of the space X and algebraic properties of the ring, C(X), of continuous functions from X into ℝ, the ordered field of real numbers.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, Gainesville, FL, 32611-8105, USA

    Robert T. Finn

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  1. Robert T. Finn
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Bowling Green State University, Bowling Green, Ohio, USA

    W. Charles Holland

  2. Caribbean Mathematics Foundation, Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Jorge Martinez

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© 1997 Springer Science+Business Media Dordrecht

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Finn, R.T. (1997). Reflections on the Global Dimensions of Rings of Continuous Functions. In: Holland, W.C., Martinez, J. (eds) Ordered Algebraic Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5640-0_2

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  • DOI: https://doi.org/10.1007/978-94-011-5640-0_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6378-4

  • Online ISBN: 978-94-011-5640-0

  • eBook Packages: Springer Book Archive

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