A Contribution To The Group Of Units' Problem In Some 2-Cyclic Refined Neutrosophic Rings

Basheer Abd Al Rida Sadiq

Al-Imam Al-Kadhum College For Islamic Science University, Iraq

e-mail: basheer.abdrida@alkadhum-col.edu.iq

Abstract

 This paper is dedicated to study the group of units problem in some 2-cyclic refined neutrosophic rings, where it presents a full classification of the group of units in 2-cyclic refined neutrosophic ring of integers  , 2-cyclic refined neutrosophic ring of integers modulo 2 and 3 ,  and 2-cyclic refined neutrosophic ring of real numbers , as direct products of the cyclic groups. On the other hand, this work provides a necessary and sufficient condition for the invertibility of any square 2-cyclic refined neutrosophic real matrix.

Also, we will illustrate some examples to clarify the validity of our work.

Keywords: 2-cyclic refined rings; group of units; invertible, neutrosophic ring.