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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 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.

Invariance groups of finite functions and orbit equivalence of permutation groups

Eszter K. Horváth, Géza Makay, Reinhard Pöschel, Tamás Waldhauser (2015)

Open Mathematics

Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections...

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