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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1066,
author = {Milan Jasem},
title = {On lattice-ordered monoids},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {23},
year = {2003},
pages = {101-114},
zbl = {1072.06010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1066}
}
Milan Jasem. On lattice-ordered monoids. Discussiones Mathematicae - General Algebra and Applications, Tome 23 (2003) pp. 101-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1066/
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