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Decomposition of commutative ordered Γ-semigroups into archimedean components

Authors
  • Siripitukdet, M.1
  • Iampan, A.1
  • 1 Naresuan University, Department of Mathematics, Faculty of Science, Phitsanulok, 65000, Thailand , Phitsanulok (Thailand)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Jan 01, 2008
Volume
29
Issue
1
Pages
40–46
Identifiers
DOI: 10.1134/S1995080208010095
Source
Springer Nature
Keywords
License
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Abstract

We can see that any semigroup can be considered as a Γ-semigroup. In this paper, we first introduce the relation “η” on ordered Γ-semigroups and prove that for commutative ordered Γ-semigroups, we have the usual relation N is equal to the relation η. It is shown that if M is commutative, then M is, uniquely, an ordered semilattice of archimedean sub-Γ-semigroups which means that it is decomposable, in a unique way, into its archimedean components.

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