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

Nabil Khuder Salman^1,*, Maikel Leyva Vazquez², Batista Hernández Noel³

¹AL-Farahidi University, Baghdad, Iraq

²Universidad Regional Autónoma de los Andes Sede Babahoyo (UNIANDES Babahoyo). Ecuador

³Universidad Regional Autónoma de los Andes (UNIANDES Babahoyo), Ecuador

Emails: nsalman@uoalfarahidi.edu.iq; direccionbabahoyo@uniandes.edu.ec; ub.coordinacionac@uniandes.edu.ec

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 real/rational 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.

Keywords: 3-cyclic refined neutrosophic ring; 4-cyclic refined neutrosophic ring; Von Shtawzen's group; group of units