Displaying similar documents to “Expansion of an atomic operator.”

A characterization of complete atomic Boolean algebra.

Francesc Esteva (1977)

Stochastica

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In this note we give a characterization of complete atomic Boolean algebras by means of complete atomic lattices. We find that unicity of the representation of the maximum as union of atoms and Lambda-infinite distributivity law are necessary and sufficient conditions for the lattice to be a complete atomic Boolean algebra.

A representation theorem for certain Boolean lattices.

José Ríos Montes (1988)

Publicacions Matemàtiques

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Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.

Boolean powers

P. Ribenboin (1969)

Fundamenta Mathematicae

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Zero-dimensional Dugundji spaces admit profinite lattice structures

Lutz Heindorf (1992)

Commentationes Mathematicae Universitatis Carolinae

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We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.