Displaying similar documents to “A non commutative generalization of ☆ -autonomous lattices”

Interior and closure operators on bounded residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2014)

Open Mathematics

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Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and...

Radicals and complete distributivity in relatively normal lattices

Jiří Rachůnek (2003)

Mathematica Bohemica

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Lattices in the class ℐℛ𝒩 of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in ℐℛ𝒩 the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in ℐℛ𝒩 with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity...

Interior and Closure Operators on Commutative Bounded Residuated Lattices

Jiří Rachůnek, Zdeněk Svoboda (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Commutative bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate additive closure and multiplicative interior operators on this class of algebras.