# 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} }

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 DR`monoids 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

- Mathematics
- 2008

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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