On lattice-ordered monoids

Milan Jasem

Discussiones Mathematicae - General Algebra and Applications (2003)

  • Volume: 23, Issue: 2, page 101-114
  • ISSN: 1509-9415

Abstract

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In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered 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 ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient 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, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.

How to cite

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Milan Jasem. "On lattice-ordered monoids." Discussiones Mathematicae - General Algebra and Applications 23.2 (2003): 101-114. <http://eudml.org/doc/287761>.

@article{MilanJasem2003,
abstract = {In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered 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 ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient 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, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.},
author = {Milan Jasem},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {lattice-ordered monoid; normal lattice-ordered monoid; dually residuated lattice-ordered semigroup; direct decomposition; polar},
language = {eng},
number = {2},
pages = {101-114},
title = {On lattice-ordered monoids},
url = {http://eudml.org/doc/287761},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Milan Jasem
TI - On lattice-ordered monoids
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2003
VL - 23
IS - 2
SP - 101
EP - 114
AB - In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered 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 ∈ A and na ≥ 0 for some positive integer n imply a ≥ 0. A necessary and sufficient 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, to be the direct product of the lattice-ordered group I and a lattice-ordered semigroup P with the least element 0.
LA - eng
KW - lattice-ordered monoid; normal lattice-ordered monoid; dually residuated lattice-ordered semigroup; direct decomposition; polar
UR - http://eudml.org/doc/287761
ER -

References

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