AG_^-GRUPOID BERINVERS LENGKAP

FAJAR NUR AHMAD , Dr. Yeni Susanti. S.Si., M.Si.

2016 | Skripsi | S1 MATEMATIKA

Sebarang grupoid (S, *) dengan setiap a, b, c di dalam S memenuhi (a*b)*c = (c*b)*a disebut AGL-grupoid. Selanjutnya AGL-grupoid S yang memenuhi a*(b*c) = b*(a*c) untuk setiap a, b, c elemen S disebut AG**L-grupoid. AG**L-grupoid S dikatakan berinvers lengkap jika setiap a di dalam S terdapat a' di dalam S sehingga (a*a')*a = a dan a*a' = a'*a. Dalam skripsi ini dibahas tentang sifat-sifat dari AGL-grupoid, dan bentuk khususnya yaitu AGL-grup, AG**L-grupoid, maupun AG**L-grupoid berinvers lengkap. Selanjutnya disajikan beberapa jenis relasi kongruensi pada AG**L-grupoid berinvers lengkap dan ditunjukkan bahwa kelas relasi kongruensi tersebut pada AG**L-grupoid berinvers lengkap membentuk suatu semilattice, AGL-grup, maupun E-uniter. Lebih lanjut ditunjukkan bahwa himpunan relasi kongruensi pada AG**L-grupoid berinvers lengkap yaitu semilattice kongruen, AGL-grup kongruen, maupun E-uniter kongruen membentuk suatu lattice lengkap.

Any groupoid S which satisfies the identity (a*b)*c = (c*b)*a for all a, b, c in S is called an AGL-groupoid. Furthermore, an AGL-grupoid which satisfies the identity a*(b*c) = b*(a*c) for all a, b, c in S is called an AG**L - groupoid. An AG**L-groupoid S is said to be completely inverse if for every a in S there exists a' in S such that (a*a')*a = a and a*a' = a'*a. In this thesis it is investigated the properties of AGL-groupoids and particular forms; namely : AGL-groups, AG**L-groupoids, and completely inverse AG**L-groupoids. This thesis provides several types of congruence relations on a completely inverse AG**L-groupoid and it is shown that those classes of congruence relation on a completely inverse AG**L -groupoid form semilattices, AGL-groups, and E-unitaries. Furthermore, it is shown that the set of the congruence relation on a completely inverse AG**L-groupoid; namely : semilattice congruence, AGL-group congruence, and Eunitary congruence, form a complete lattice.

Kata Kunci : AG-grupoid, AG^-grupoid berinvers lengkap, E-uniter kongruen