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.

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.

Ideals of noncommutative D R ℓ -monoids

Jan Kühr (2005)

Czechoslovak Mathematical Journal

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In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one correspondence.