IJPAM: Volume 101, No. 1 (2015)

SOME REGULAR EQUIVALENCE RELATION ON
THE SEMIHYPERGROUP OF THE PARTIAL
TRANSFORMATION SEMIGROUP ON
A SET AND LOCAL SUBSEMIHYPERGROUPS
WITH THAT REGULAR EQUIVALENCE RELATION

Ruangvarin Intarawong Sararnrakskul$^1$, Sajee Pianskool$^2$
$^1$Department of Mathematics
Faculty of Science
Srinakharinwirot University
Bangkok, 10110, THAILAND
$^2$Department of Mathematics and Computer Science
Faculty of Science
Chulalongkorn University
Bangkok, 10330, THAILAND


Abstract. A hyperoperation $\circ$ on a nonempty set $H$ is a function from $H\times H$ into $P^{\ast}(H)$ where $P^{\ast}(H)$ is the set of all nonempty subset of $H$ and $(H,\circ)$ is call a hypergroupoid. A hypergroupoid $(H,\circ)$ is called a semihypergroup if the hyperoperation $\circ$ is associative. Thus, semihypergroups generalize semigroups. Moreover, if $S$ is a semigroup; we can define a hyperoperation $\circ$ on $S$ in order to make $(S,\circ)$ a semihypergroup. In 2013, R.I. Sararnrakskul defined a hyperoperation $\circ$ on the partial transformation semigroup $P(X)$ to make a semihypergroup. In this paper, we define a regular equivalence relation $\rho$ on $(P(X),\circ)$ so that $P(X)/\rho$ is a semihypergroup and then we studies some subsemihypergroup of $P(X)/\rho$.

Received: November 10, 2014

AMS Subject Classification: 20M20, 20N20

Key Words and Phrases: partial transformation semigroup, local subsemigroup, semihypergroup, regular equivalence relation

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DOI: 10.12732/ijpam.v101i1.3 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: 101
Issue: 1
Pages: 21 - 31


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