RELASI GREEN DAN REGULARITAS PADA SEMIGRUP TRANSFORMASI YANG MENGAWETKAN URUTAN DAN RELASI EKUIVALENSI DUA ARAH; GREEN’S RELATIONS AND REGULARITY FOR SEMIGROUPS OF TRANSFORMATIONS THAT PRESERVE ORDER AND A DOUBLE DIRECTION EQUIVALENCE

BAYU KHARISMA ADHIATMA, Yeni Susanti

2015 | Skripsi | FMIPA

Let X be a non-empty set and let E be an equivalence relation on X. The set of all mappings from X into X under composition is a semigroup and denoted by TX. The semigroup TX is called full transformation semigroup. Let TE?(X) be the set of all elements in TX that preserve E in double direction. This set forms a subsemigrup in TX. For totally ordered set X, we define OE?(X) as the set of all elements in TE?(X) that preserve the order. The set OE?(X) forms a subsemigrup of TE?(X) i.e. also a subsemigrup of TX. In this thesis, we discuss the Green’s relations in OE?(X). Moreover it is showed that OE?(X) is a regular semigroup.

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