IJPAM: Volume 89, No. 1 (2013)
ON
-MINIMAL
-IDEALS IN AN ORDERED SEMIGROUP


Thawhat Changphas
Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND
Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen, 40002, THAILAND
Abstract. In this paper, we introduce an equivalence relation on an ordered semigroup
. Using the relation
defined, we characterize
-minimal
-ideals of
. Several sufficient conditions are presented for
-minimal left ideals and
-minimal right ideals of
to be
-minimal
-ideals of
. 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, -regular, center, ideal, nilpotent ideal, left (right) ideal, bi-ideal,
-ideal,
-minimal
-ideal,
-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