IJPAM: Volume 100, No. 1 (2015)

ON $(m,n)$-IDEALS OF AN ORDERED SEMIGROUP

Thawhat Changphas
Department of Mathematics, Faculty of Science
Khon Kaen University, Khon Kaen, 40002, THAILAND
Centre of Excellence in Mathematics, CHE
Si Ayutthaya Rd., Bangkok 10400, THAILAND


Abstract. In this paper we introduce the concept of $(m,n)$-simple ordered semigroups extending the notion of simple ordered semigroups, and prove that an ordered semigroup $(S,\cdot,\le)$ does not contain proper $(m,n)$-ideals if and only if it is both $(m,0)$-simple and $(0,n)$-simple.

Received: July 8, 2014

AMS Subject Classification: 06F05

Key Words and Phrases: semigroup, ordered semigroup, left simple, right simple, bi-ideal, $(m,n)$-ideal, $(m,n)$-simple

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DOI: 10.12732/ijpam.v100i1.1 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 100
Issue: 1
Pages: 1 - 5


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