On NeutroQuadrupleRings
Muritala Abiodun Ibrahim, Agboola Adesina Abdul Akeem, Zulaihat Hassan-Ibrahim, Emmanuel O. Adeleke · Advances in computer and electrical engineering book series · 2022
In an attempt to generalize and create alternatives for classical algebraic structures, Smarandache in 2019 introduced the idea of treating binary operations on sets as partially well (totally outer) defined with axioms that are partially true (totally false) and even indeterminate for some elements of any given algebraic structure. The structures formed with these types of operations called Neutro(Anti) Operations are called Neutro(Anti) Structures and are named according to the axioms that are neutro(anti)-sophicated. In this chapter, the authors consider some properties of neutrosophic quadruple numbers with examples. In particular, they introduce and study the concept of NeutroQuadrupleRings and their substructures. Some basic definitions and a few important results are presented. It is shown that the intersection and union of any two NeutroQuadrupleSubrings of a particular class does not necessarily belong to the same class. Also, they give a necessary and sufficient condition for a neutrosophic quadruple ring (NQ(X), +, ·) to be a NeutroQuadrupleRing.