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Spectral Theory of Continuous Lattices

In: A Compendium of Continuous Lattices

Author

Listed:
  • Gerhard Gierz

    (Technische Hochschule Darmstadt, Fachbereich Mathematik)

  • Karl Heinrich Hofmann

    (Tulane University, Department of Mathematics)

  • Klaus Keimel

    (Technische Hochschule Darmstadt, Fachbereich Mathematik)

  • Jimmie D. Lawson

    (Louisiana State University, Department of Mathematics)

  • Michael W. Mislove

    (Tulane University, Department of Mathematics)

  • Dana S. Scott

    (Merton College)

Abstract

Opectral theory plays an important and well-known role in such areas as the theory of commutative rings, lattices, and of C*-algebras, for example. The general idea is to define a notion of “prime element” (more often: ideal element) and then to endow the set of these primes with a topology. This topological space is called the “spectrum” of the structure. One then seeks to find how algebraic properties of the original structure are reflected in the topological properties of the spectrum; in addition, it is often possible to obtain a representation of the given structure in a concrete and natural fashion from the spectrum.

Suggested Citation

  • Gerhard Gierz & Karl Heinrich Hofmann & Klaus Keimel & Jimmie D. Lawson & Michael W. Mislove & Dana S. Scott, 1980. "Spectral Theory of Continuous Lattices," Springer Books, in: A Compendium of Continuous Lattices, chapter 0, pages 237-270, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-67678-9_6
    DOI: 10.1007/978-3-642-67678-9_6
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