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

Jan Kühr

Displaying similar documents to “Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids”

Lexicographic extensions of dually residuated lattice ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Mathematica Bohemica

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Dually residuated lattice ordered monoids ( $D R ℓ$ -monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings ( $M V$ -algebras, $B L$ -algebras) and their non-commutative variants ( $G M V$ -algebras, pseudo $B L$ -algebras). In the paper, lex-extensions and lex-ideals of $D R ℓ$ -monoids (which need not be commutative or bounded) satisfying a certain natural condition are studied.

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.

Spectral topologies of dually residuated lattice-ordered monoids

Jan Kühr (2004)

Mathematica Bohemica

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Dually residuated lattice-ordered monoids ( $D R ℓ$ -monoids for short) generalize lattice-ordered groups and include for instance also $G M V$ -algebras (pseudo $M V$ -algebras), a non-commutative extension of $M V$ -algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.

Displaying similar documents to “Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids”

Lexicographic extensions of dually residuated lattice ordered monoids

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

Spectral topologies of dually residuated lattice-ordered monoids

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