• DOI:10.7151/DMGAA.1066
• Corpus ID: 14714474

On lattice-ordered monoids

@article{Jasem2003OnLM,
  title={On lattice-ordered monoids},
  author={Milan Jasem},
  journal={Discussiones Mathematicae General Algebra and Applications},
  year={2003},
  volume={23},
  pages={101-114}
}

• M. Jasem
• Published 2003
• Mathematics
• Discussiones Mathematicae General Algebra and Applications

In the paper lattice-ordered monoids and specially normal latticeordered monoids which are a generalization of dually residuated latticeordered semigroups are investigated. Normal lattice-ordered monoids are metricless normal lattice-ordered autometrized algebras. It is proved that in any lattice-ordered monoid A, a 2 A and na ‚ 0 for some positive integer n imply a ‚ 0. A necessary and su‐cient condition is found for a lattice-ordered monoid A, such that the set I of all invertible elements of A is a convex subset of A and A i µ I, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.