IJPAM: Volume 98, No. 5 (2015)

ON INTRA REGULAR ORDERED SEMIGROUPS

D. Kanthakumar$^1$, P. Nandakumar$^2$
$^1$Department of Mathematics
Research and Development Centre
Bharathiar University
Coimbatore, 641 046, INDIA
$^2$Perunthalaivar Kamarajar Institute of Engineering and Technology
Karaikal, 609 603 (U.T.of Puducherry), INDIA


Abstract. In this paper, we discuss some properties of intra regular semigroups. We obtain equivalent condition for a semigroup to be intra regular. We have shown that if $M$ is an ideal of an intra regular ordered semigroup $S$ then $M$ is completely prime. We have shown that if $A$ is an ideal of a semigroup $S$ and if $B$ is any subset of $S$ then $(A: B)$ is an ideal of $S.$

Received: January 29, 2015

AMS Subject Classification: 06F05, 20M17, 16D25

Key Words and Phrases: ordered semigroups and monoids, regular semigroup, ideals

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DOI: 10.12732/ijpam.v98i5.5 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: 98
Issue: 5
Pages: 27 - 31


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