Vector lattices, Boolean rings and simple functions
Topping, D. (1964)
Portugaliae mathematica
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Topping, D. (1964)
Portugaliae mathematica
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M. Lambrou (1983)
Fundamenta Mathematicae
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Leopoldo Nachbin (1949)
Fundamenta Mathematicae
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Josef Niederle (1989)
Czechoslovak Mathematical Journal
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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.
Janowitz, M.F., Coté, N.H. (1976)
Portugaliae mathematica
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Zhi-qiang Liu (2024)
Kybernetika
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In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained.
Bohuslav Sivák (1982)
Mathematica Slovaca
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