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. 
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LEXICOGRAPHIC EXTENSIONS OF DUALLY RESIDUATED LATTICE ORDERED MONOIDS
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,…
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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…
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