The Order of the Set of -Class for Semigroup of Order-Preserving and Order-Decreasing Partial Transformation

Mbah Moses Anayo, Ugbene Ifeanyichukwu Jeff, Bakare Getta Naimat

Abstract: The major problems usually encountered by transformation semigroup is that of enumeration Umar, 2010. Here we studied the elements of partial transformation and extracted those that are order-preserving and order-decreasing which is a subsemigroup of partial transformation. Thus we listed the elements that satisfy the -class for. A general order of obtaining the set of -class for was obtained.

Keywords: class, Greens relation, order-preserving and order-decreasing partial transformation semigroup, partial transformation semigroup