SOME REGULAR EQUIVALENCE RELATION ON THE SEMIHYPERGROUP OF THE PARTIAL TRANSFORMATION SEMIGROUP ON A SET AND LOCAL SUBSEMIHYPERGROUPS WITH THAT REGULAR EQUIVALENCE RELATION
R.I. Sararnrakskul, Sajee Pianskool · International Journal of Pure and Apllied Mathematics · 2015
A hyperoperation • on a nonempty set H is a function from H × H into P * (H) where P * (H) is the set of all nonempty subset of H and (H, •) is call a hypergroupoid.A hypergroupoid (H, •) is called a semihypergroup if the hyperoperation • is associative.Thus, semihypergroups generalize semigroups.Moreover, if S is a semigroup; we can define a hyperoperation • on S in order to make (S, •) a semihypergroup.In 2013, R.I. Sararnrakskul defined a hyperoperation • on the partial transformation semigroup P (X) to make a semihypergroup.In this paper, we define a regular equivalence relation ρ on (P (X), •) so that P (X)/ρ is a semihypergroup and then we studies some subsemihypergroup of P (X)/ρ.