Radikal Prima dan Radikal Prima Lengkap dalam Semiring Ternary

RATNA SARI W, Dr.rer.nat. Ari Suparwanto, M.Si.

2016 | Tesis | S2 Matematika

Semiring ternary adalah semigrup komutatif terhadap operasi penjumlahan dan semigrup terhadap operasi ternary perkalian serta berlaku distributif kanan, kiri dan lateral terhadap operasi penjumlahan dan perkalian. Di dalam tesis ini dibahas radikal prima dan radikal prima lengkap dalam semiring ternary. Jika A ideal dari semiring ternary T, maka irisan dari semua ideal prima dari T yang memuat A disebut radikal prima A. Sedangkan radikal prima lengkap adalah irisan semua ideal prima lengkap dari T yang memuat A. Selain itu juga dibahas hubungan antara ideal prima, ideal prima lengkap, ideal semiprima dan ideal semiprima lengkap dengan radikal prima dan radikal prima lengkap dalam semiring ternary.

A ternary semirings is an additive commutative semigroup, multiplication ternary semigroup and its satisfies lateral, right and left distibutives. In this tesis we will discussed about prime radicals and completely prime radicals in ternary semirings, properties and its theorem. If A is an ideals of a ternary semiring T, then the intersection of all prime ideals of T containing A is called prime radicals. A completely prime radicals is the intersection of all completely prime ideals of T containing A. Also, we will discussed about the relation in terms of prime ideals, completely prime ideals, semiprime ideals and completely semiprime ideals with prime radicals and completely prime radicals in ternary semirings.

Kata Kunci : ideal prima, ideal prima lengkap, ideal semiprima, ideal semiprima lengkap, radikal prima, radikal prima lengkap, semiring ternary / prime ideals, completely prime ideals, semiprime ideals, completely semiprime ideals, prime radicals, completely prime rad