Lexicographic extensions of dually residuated lattice ordered monoids

Jiří Rachůnek; Dana Šalounová

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 $A$ .

Dually residuated $ℓ$ -monoids having no non-trivial convex subalgebras

Jan Kühr (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this note we describe the structure of dually residuated $ℓ$ -monoids ( $𝐷𝑅 ℓ$ -monoids) that have no non-trivial convex subalgebras.

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

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

Dually residuated ℓ -monoids having no non-trivial convex subalgebras

Dually residuated $ℓ$ -monoids having no non-trivial convex subalgebras