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Displaying similar documents to “Negation in bounded commutative D R ℓ -monoids”

Interior and closure operators on bounded residuated lattice ordered monoids

Filip Švrček (2008)

Czechoslovak Mathematical Journal

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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.

Representable dually residuated lattice-ordered monoids

Jan Kühr (2003)

Discussiones Mathematicae - General Algebra and Applications

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Dually residuated lattice-ordered monoids (DRl-monoids) generalize lattice-ordered groups and include also some algebras related to fuzzy logic (e.g. GMV-algebras and pseudo BL-algebras). In the paper, we give some necessary and sufficient conditions for a DRl-monoid to be representable (i.e. a subdirect product of totally ordered DRl-monoids) and we prove that the class of representable DRl-monoids is a variety.

Direct decompositions of dually residuated lattice-ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Discussiones Mathematicae - General Algebra and Applications

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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.

A duality between algebras of basic logic and bounded representable D R l -monoids

Jiří Rachůnek (2001)

Mathematica Bohemica

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B L -algebras, introduced by P. Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that B L -algebras are the duals of bounded representable D R l -monoids. This duality enables us to describe some structure properties of B L -algebras.