Some Special Refined Neutrosophic Ideals in Refined Neutrosophic Rings: A Proof-of-Concept Study

Abstract

In this research, we created notions of a refined neutrosophic prime (completely prime, semiprime, and completely semiprime) ideal in a refined neutrosophic ring. If R(I₁, I₂) is a refined neutrosophic ring, then each ideal of R(I₁, I₂) has the form J+KI₁+LI₂ are ideals of the classical ring R. The objective of this work is to find the necessary and sufficient condition on classical ideals J, L and K that makes J+KI₁+LI₂ a prime (completely prime, semiprime, and completely semiprime) ideal in R(I₁, I₂). We studied some of the elementary properties of these concepts and the most important properties that link them.