Spectral Theory of Continuous Lattices

Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove and Dana S. Scott
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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

Chapter Chapter V in A Compendium of Continuous Lattices, 1980, pp 237-270 from Springer

Abstract: 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.

Keywords: Complete Lattice; Prime Element; Heyting Algebra; Continuous Lattice; Irreducible Element (search for similar items in EconPapers)
Date: 1980
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DOI: 10.1007/978-3-642-67678-9_6

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