Displaying similar documents to “Lexicographic extensions of dually residuated lattice ordered monoids”

Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids

Jan Kühr (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Lattice-ordered groups, as well as G M V -algebras (pseudo M V -algebras), are both particular cases of dually residuated lattice-ordered monoids ( D R ℓ -monoids for short). In the paper we study ideals of lower-bounded D R ℓ -monoids including G M V -algebras. Especially, we deal with the connections between ideals of a D R ℓ -monoid A and ideals of the lattice reduct of A .

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.