IJPAM: Volume 86, No. 3 (2013)

SOME LOCAL SUBSEMIHYPERGROUPS OF
THE PARTIAL TRANSFORMATION SEMIGROUP ON A SET

Ruangvarin Intarawong Sararnrakskul
Department of Mathematics
Faculty of Science
Srinakharinwirot University
Bangkok, 10110, THAILAND


Abstract. In this paper, we give definitions of a local subset and a local subsemihypergroup of a semihypergroup. Moreover, we define a hyperoperation • on the partial transformation semigroup P(X) so that (P(X),•) is a semihypergroup. Our aim is to characterize in form of an idempotent α of the semigroup P(X) when the local subset &alphal• G(X)•α of (P(X),•) become a local subsemihypergroup of P(X).

Received: May 22, 2013

AMS Subject Classification: 20M20, 20N20

Key Words and Phrases: partial transformation semigroup, local subsemigroup, hypergroup, semihypergroup

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DOI: 10.12732/ijpam.v86i3.10 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: 86
Issue: 3