On lattice-ordered monoids

• Autorzy: Milan Jasem
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

lattice-ordered monoid; normal lattice-ordered monoid; dually residuated lattice-ordered semigroup; direct decomposition; polar

Kategorie tematyczne

• 06F05: Ordered semigroups and monoids

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2003
• Tom: 23
• Numer: 2
• Strony: 101-114

Daty

wydano

2003

otrzymano

2002-11-26

otrzymano

2003-05-16

otrzymano

2003-12-20

Twórcy

autor

Milan Jasem

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

Bibliografia

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Identyfikatory

DOI

10.7151/dmgaa.1066