# Direct decompositions of dually residuated lattice-ordered monoids

@article{Rachunek2004DirectDO,
title={Direct decompositions of dually residuated lattice-ordered monoids},
author={Jir{\'i} Rachunek and Dana Salounov{\'a}},
journal={Discussiones Mathematicae General Algebra and Applications},
year={2004},
volume={24},
pages={63-74}
}
• Published 2004
• Mathematics
• Discussiones Mathematicae General Algebra and Applications
The class of dually residuated lattice ordered monoids (DR-monoids) contains, in an appropriate signature, all -groups, Brouwerian algebras, MV and GMV -algebras, BLand pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRmonoids in general and we characterize ideals of DR-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DR-monoids.
3 Citations
LEXICOGRAPHIC EXTENSIONS OF DUALLY RESIDUATED LATTICE ORDERED MONOIDS
• Mathematics
• 2004
Dually residuated lattice ordered monoids (DR-monoids) are common generalizations of, e.g., lattice ordered groups, Brouwerian algebras and algebras of logics behind fuzzy reasonings (MV -algebras,
Direct product decompositions of bounded commutative residuated ℓ-monoids
The notion of bounded commutative residuated ℓ-monoid (BCR ℓ-monoid, in short) generalizes both the notions of MV-algebra and of BL-algebra. Let be a BCR ℓ-monoid; we denote by ℓ() the underlying
Direct product factors in GMV-algebras
• Mathematics
• 2005
GMV-algebras are non-commutative generalizations of MV-alge­ bras and by A. Dvurecenskij they can be represented as intervals of unital lattice ordered groups. Moreover, they are polynomially

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