Direct Product of Complex Neutrosophic Subrings

Abstract

The complex neutrosophic set is a generalization of the neutrosophic set with the addition of three phase terms. The complex neutrosophic set deals with periodic data that contains uncertainty, indeterminacy, and falsity. The complex neutrosophic set has a variety of applications, such as signal processing, hospital infrastructure design, medical image denoising, segmentation distance measurement, and the game of loser, neutral, and winner. This article presents a novel concept for complex neutrosophic subrings and illustrates how these subrings can generate two other neutrosophic subrings. Additionally, we prove that the intersection of two neutrosophic subrings is a neutrosophic subring. We expand this idea to talk about the abstraction of level subsets of complex neutrosophic sets and look into the basic algebraic properties of this event. We prove that the level subset of the complex neutrosophic subring is a subring. Moreover, we demonstrate that the product of two complex neutrosophic subrings is also a complex neutrosophic subring and explore some novel consequences about the direct product of complex neutrosophic subrings. Our findings generalize and extend the existing ring theory results within a complex neutrosophic framework.