On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group

Abstract

This paper aims to solve the group of units problem for 3-cyclic real and rational refined neutrosophic rings and 4-cyclic real and rational refined neutrosophic rings, where ring isomorphisms between the realrational 3-cyclic and 4-cyclic refined neutrosophic rings and the direct product of some field extensions of Q and R. These isomorphisms will help in classifying the group of units of each studied ring in terms of direct products of classical well-known abelian groups. Also, we use the classification isomorphisms to determine all ideals in these classes of algebraic rings.