Finite-valued dually residuated lattice-ordered monoids

Jan Kühr

Displaying similar documents to “Finite-valued dually residuated lattice-ordered monoids”

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.

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 $A$ .

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.