KONGRUENSI IDEMPOTENT-SEPARATING MAKSIMUM PADA p-SEMIGRUP REGULER;THE MAXIMUM IDEMPOTENT-SEPARATING CONGRUENCE IN p-SEMIGRUP REGULER

FITRIANI, Sri Wahyuni

2011 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

Semigroup is a structure with a associative binary operation. Since semigroup may not have an identity element and invers element, there is a regularity characteristic of element in semigroup. If all of the element of semigroup have regularity, then this semigroup is called regular semigroup. ?-regular semigroup is one of the class regular semigroups. It is a pair of regular semigroup with the set of idempotent elements which satifies some axioms. If the first axiom in the definition of ?-regular semigroup which explained about commutative law for idempotent elements leaving out, then a new class of regular semigroup is defined, called p-regular semigroup. In this case, the set of all ?-regular semigroups is subset of the set of all p-regular semigroup. After observing the characteristic of p-regular semigroup, define a maximum idempotent-separating congruence in p-regular semigroup. This congruence is the same congruence in the pair of orthodox and band. Finally conclusion, p-regular semigroup is a generalized regular semigroup (orthodox) which has the maximum idempotent-separating congruences.

Kata Kunci : Semigrup Reguler, Kongruensi, ?-Semigrup Reguler, p-Semigrup Reguler, Kongruensi Idempotent-separating