KONSEP IDEMPOTEN, BAND, DAN RELASI GREEN PADA SEMIGRUP TERNIER

RAHMAWATI SURYA UTAMI , Dr. Budi Surodjo, M.Si.

2017 | Skripsi | S1 MATEMATIKA

Semigrup ternier merupakan generalisasi dari semigrup biner. Himpunan tak kosong S disebut semigrup ternier S jika dilengkapi operasi ternier dot : S x S x S -> S yang memenuhi dot(a,b,c)=a dot b dot c. Dalam tulisan ini, difokuskan pada sifat-sifat semigrup ternier S dan hubungan-hubungan diantara semigrup ternier S, elemen regular, elemen idempoten dan elemen invers dengan membandingkan sifat-sifat pada semigrup biner. Selanjutnya, dapat didefinisikan pula relasi Green pada semigrup ternier S yang dikonstruksi berdasarkan relasi Green pada semigrup biner. Relasi Green pada semigrup biner analog dengan relasi Green pada semigrup ternier.

Ternary semigroup is a generalization of binary semigroup. The nonempty set S is called ternary semigroup S if it is equiped with ternary operation dot : S x S x S -> S that fulfill dot(a,b,c)=a dot b dot c. In this thesis, we focus on the properties of ternary semigroup S and the relations between ternary semigroup S , the regular element, the idempotent element and the inverse element by comparing the properties of the binary semigroup. Furthermore, we can also define Green�s relations in ternary semigroup S constructed based by Green relation on binary semigroup. Green relation on binary semigroup analog with Green relation on ternary semigroup.

Kata Kunci : ternary semigroup, regular element, Green's relation