On neutrosophic ideals and prime ideals in rings

Abstract

This article aims to introduce and explore the concept of neutrosophic ideals in the context of rings. Besides, we investigate how the property of regularity in a ring can be understood through the lens of neutrosophic ideals. We further present the concept of neutrosophic prime ideals and systematically identify all neutrosophic prime ideals in $ \mathbb{Z} $.

Keywords

• neutrosophic set
• regular ring
• neutrosophic ideal
• neutrosophic prime ideal