Bi-ideal Prima Pada Semigrup Ternier

NOVA SETIAWAN, Dr. Budi Surodjo, M.Si

2018 | Skripsi | S1 MATEMATIKA

Pada skripsi ini dibahas mengenai semigrup ternier yang merupakan generalisasi dari semigrup biner. Himpunan tak kosong S disebut semigrup ternier S jika dilengkapi operasi ternier *: S x S x S -> S yang memenuhi sifat asosiatif yaitu untuk setiap a, b, c, d, e anggota S berlaku (a*b*c)*d*e = a*(b*c*d)*e = a*b*(c*d*e). Kemudian akan dijelaskan sifat-sifat dasar mengenai semigrup ternier, semigrup ternier reguler, ideal pada semigrup ternier, quasi ideal, dan bi-ideal.Selain itu juga dikaji tentang hubungan antara quasi ideal dengan bi-ideal semigrup ternier. Pada bagian akhir, akan dibahas sebuah keluarga himpunan bi-ideal prima kuat yang membentuk topologi keluarga himpunan semua bi-ideal prima pada suatu semigrup ternier yang setiap bi-idealnya idempoten.

In this paper, we will discuss about ternary semigroups which is a generalization of binary semigroups. The nonempty set S is called ternary semigroups S if it is equiped with ternary operation *: S x S x S -> S that fulfill asosiative properties that is for every a, b, c, d, e in S satisfies(a*b*c)*d*e = a*(b*c*d)*e = a*b*(c*d*e). Then, will be described the basic properties of ternary semigroups, regular ternary semigroups, ideal in ternary semigroups, quasi ideal, and bi-ideal. Furthermore, It also studied about the relationship of quasi ideal and bi-ideal of ternary semigroups. At the end will be discussed a family of set of strongly prime bi-ideals which are formed a topology to family of set of all prime bi-ideal in ternary semigroups which is every its bi-ideals are idempotent.

Kata Kunci : Bi-ideal, Bi-ideal Prima, Semigrup Ternier, Bi-ideal Prima Pada Semigrup Ternier