The Structure of Neutrosophic Radical of an ideal and Primary Ideal in Neutrosophic Rings

In this study, we define radical and primary ideals as novel types of neutrosophic substructures within a neutrosophic ring. We investigate the properties of these substructures based on the characteristics of neutrosophic rings. Finally, several examples are provided to illustrate the validity of the results. Although neutrosophic radical and primary ideals have intrinsic theoretical value, this study aims to lay the groundwork for establishing a Noether theorem on neutrosophic primary decompositions.