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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Spectra of abelian wekly associative lattice groups

100%
Rachůnek J.
Discussiones Mathematicae - General Algebra and Applications
|
2000
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tom 20
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nr 1
51-61
EN
The notion of a weakly associative lattice group is a generalization of that of a lattice ordered group in which the identities of associativity of the lattice operations join and meet are replaced by the identities of weak associativity. In the paper, the spectral topologies on the sets of straightening ideals (and on some of their subsets) of abelian weakly associative lattice groups are introduced and studied.
2
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Interior and closure operators on bounded commutative residuated l-monoids

63%
Rachůnek J., Švrček F.
Discussiones Mathematicae - General Algebra and Applications
|
2008
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tom 28
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nr 1
11-27
EN
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 (i.e., algebras of the Hájek's basic fuzzy logic) and Heyting algebras as proper subclasses.
3
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Direct decompositions of dually residuated lattice-ordered monoids

63%
Rachůnek J., Šalounová D.
Discussiones Mathematicae - General Algebra and Applications
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2004
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tom 24
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nr 1
63-74
EN
The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.
4
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Interior and closure operators on bounded residuated lattices

63%
Rachůnek J., Svoboda Z.
Open Mathematics
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2014
|
tom 12
|
nr 3
534-544
EN
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 lattices of their regular elements.
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