Ideal Prima Pada Daerah Dedekind Berupa Polinom Faktor Berderajat Satu Dari Ring Bilangan Bulat

Muklas Maulana

Fraktal: Jurnal Matematika dan Pendidikan Matematika
Vol 3 No 2 (2022): November 2022

Dedekind Domain and prime ideals are part of the topics discussed in the field of abstract algebra. An integral Domain is said to be the Dedekind Domain if and only if it is a Noetherian, integrally closed, and each of its prime ideals is a maximum ideal. In 2019, Maulana discussed the prime ideal’s properties of Gauss integers. At present, there is no research about prime ideals of specific Dedekind Domain, because of that reason, in this article we will give some prime ideals and prime ideals’ characteristics in the area of the Dedekind Domain Z[x]/<x^2>. In this article, it is found the conclusion I=<x> and I=<k,x> are prime ideals in that Dedekind Domain.