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ArticleOriginal scientific text

Title

On lattice-ordered monoids

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Chemical Technology, Slovak Technical University, Radlinského 9, 812 37 Bratislava, Slovak Republic

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.

Keywords

ENG
lattice-ordered monoid, normal lattice-ordered monoid, dually residuated lattice-ordered semigroup, direct decomposition, polar

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Discussiones Mathematicae - General Algebra and Applications
2003/23/2
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Pages:
101-114
Main language of publication
English
Received
2002-11-26
Published
2003

DOI: 10.7151/dmgaa.1066

Exact and natural sciences