KARAKTERISASI E ï SEMIGRUPCHARACTERIZATION OF E ïSEMIGROUP
Dhian Arista Istikomah, S.U Sri Wahyuni · 2012
The set of idempotent elements in a semigroup motivates the emergence E i�semigroup which is a generalization of the orthodox semigroup. As an orthodox semigroup which has strong relations with regular semigroup, E i�semigroup has strong relations with E i�inversive semigroup which is generalization of the regular semigroup. To characterize E i�semigroup we use the properties of E i�inversive semigroup, sandwitsch set and weakly inverses set. In this thesis we will show that if S is an E i� inversive semigroup then there are statements about E i� semigroup, sandwich set, and weakly inverses set from the elements of S which are equivalent. Then, the concept of an E i� inversive and E i�semigroup will lead the concept of E i�inversive E i�semigroup. The last we observe about the relation of Mitsch order i� , Lallement order i�¬ and i�µ relation which are closely related to the formation of idempotent elements set become a normal band. Normal band is one of the example of E i� semigroup, so the relation about Mitsch order i� , Lallement order i�¬ and i�µ relation became a condition of idempotent elements set to be a E i�semigroup.