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Interior and closure operators on bounded commutative residuated l-monoids

Jiří Rachůnek, Filip Švrček (2008)

Discussiones Mathematicae - General Algebra and Applications

Topological Boolean algebras are generalizations of topological spaces defined by means of topological closure and interior operators, respectively. The authors in [14] generalized topological Boolean algebras to closure and interior operators of MV-algebras which are an algebraic counterpart of the Łukasiewicz infinite valued logic. In the paper, these kinds of operators are extended (and investigated) to the wide class of bounded commutative Rl-monoids that contains e.g. the classes of BL-algebras...

Interior and closure operators on bounded residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2014)

Open Mathematics

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 on the residuated...

Interior and closure operators on bounded residuated lattice ordered monoids

Filip Švrček (2008)

Czechoslovak Mathematical Journal

G M V -algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior G M V -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on D R l -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on G M V -algebras.

Interior and Closure Operators on Commutative Bounded Residuated Lattices

Jiří Rachůnek, Zdeněk Svoboda (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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.

Inverse topology in MV-algebras

Fereshteh Forouzesh, Farhad Sajadian, Mahta Bedrood (2019)

Mathematica Bohemica

We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra A and show that the set of all minimal prime ideals of A , namely Min ( A ) , with the inverse topology is a compact space, Hausdorff, T 0 -space and T 1 -space. Furthermore, we prove that the spectral topology on Min ( A ) is a zero-dimensional Hausdorff topology and show that the spectral topology on Min ( A ) is finer than the inverse topology on Min ( A ) . Finally, by open sets of the inverse topology, we define and study a congruence relation...

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