KONGRUENSI BAND DAN BAND PERSEGI DI E-SEMIGRUP E-INVERSIVE BAND AND RECTANGULAR BAND CONGRUENCE ON E-INVERSIVE E-SEMIGROUP

ASWAR ANAS, Budi Surodjo

2012 | Disertasi | PROGRAM STUDI S2 ILMU MATEMATIKA

Semigroup is one of the important part in algebra. The research in this semigroup evolve quickly, one of them is an E-inversive E-semigroup. The E-inversive E-semigroups have a characteristic that is for each idempotent element in this semigroup we form a subsemigroup. Moreover for each element in this semigroup there exists another element which mutually for on biner operation also result idempotent element. We discuss some properties of semigroup ie, if this semigroup completed by a congruence, then the congruence can be a band congruence, a rectangular band congruence, a regular congruence, a semilattice congruence, a least group congruence and etc. To form band and rectangular band congruence it is required some properties, that is weakly inverse set, inverse set, idempotent set, and inversive set . A band congruence on E-inversive E-semigroup can be obtained if this semigroup contains Green's relation R or L. Moreover, if the congruence which applied in the set of idempotent that contained in this semigroup is a rectangular band, than that congruence can be expanded in that semigroup

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