Displaying similar documents to “Dually residuated ℓ -monoids having no non-trivial convex subalgebras”

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.

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 .

Direct decompositions of dually residuated lattice-ordered monoids

Jiří Rachůnek, Dana Šalounová (2004)

Discussiones Mathematicae - General Algebra and Applications

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The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.

On ideals of lattice ordered monoids

Milan Jasem (2007)

Mathematica Bohemica

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In the paper the notion of an ideal of a lattice ordered monoid A is introduced and relations between ideals of A and congruence relations on A are investigated. Further, it is shown that the set of all ideals of a soft lattice ordered monoid or a negatively ordered monoid partially ordered by inclusion is an algebraic Brouwerian lattice.