Spectral Theory of Continuous Lattices
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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.
KeywordsComplete Lattice Prime Element Heyting Algebra Continuous Lattice Irreducible Element
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