IJPAM: Volume 89, No. 1 (2013)

ON $0$-MINIMAL $(m,n)$-IDEALS IN AN ORDERED SEMIGROUP

Thawhat Changphas
Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND


Abstract. In this paper, we introduce an equivalence relation ${\mathcal B}$ on an ordered semigroup $S$. Using the relation ${\mathcal B}$ defined, we characterize $0$-minimal $(m,n)$-ideals of $S$. Several sufficient conditions are presented for $0$-minimal left ideals and $0$-minimal right ideals of $S$ to be $0$-minimal $(m,n)$-ideals of $S$. The results obtained generalize the results on semigroups without order.

Received: June 19, 2013

AMS Subject Classification: 06F05

Key Words and Phrases: semigroup, ordered semigroup, $(m,n)$-regular, center, ideal, nilpotent ideal, left (right) ideal, bi-ideal, $(m,n)$-ideal, $0$-minimal $(m,n)$-ideal, $0$-minimal left (right) ideal

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DOI: 10.12732/ijpam.v89i1.8 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: 2013
Volume: 89
Issue: 1