A characterization of polarities whose lattice of polars is Boolean
František Šik (1981)
Czechoslovak Mathematical Journal
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František Šik (1981)
Czechoslovak Mathematical Journal
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Tabuev, S.N. (2003)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Jaromír Duda (1990)
Mathematica Slovaca
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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.
P. Ribenboin (1969)
Fundamenta Mathematicae
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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.