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A Dauns-Hofmann Theorem for Taf-Algebras

Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1379-1385

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Abstract : Let A be a TAF-algebra, Z(A) the centre of A, Id(A) the ideal lattice of A, and Mir(A) the space of meet-irreducible elements of Id(A), equipped with the hull-kernel topology. It is shown that Mir(A) is a compact, locally compact, second countable, T $_{0}$ -space, that Id(A) is an algebraic lattice isomorphic to the lattice of open subsets of Mir(A), and that Z(A) is isomorphic to the algebra of continuous, complex functions on Mir(A). If A is semisimple, then Z(A) is isomorphic to the algebra of continuous, complex functions on Prim(A), the primitive ideal space of A. If A is strongly maximal, then the sum of two closed ideals of A is closed.

Keyword : Primary 46K50, 47D25

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