On the Conditions of Imperfect Neutrosophic Duplets and Imperfect Neutrosophic Triplets

Abstract

In any neutrosophic ring R(I), an imperfect neutrosophic duplet consists of two elements x,y with a condition xy=yx=x and an imperfect neutrosophic triplet consists of three elements x,y,z with condition xy=yx=x,yz=zy=z,and xz=zx=y. The objective of this paper is to determine the necessary and sufficient conditions for neutrosophic duplets and triplets in any neutrosophic ring R(I), and to determine all triplets in Z(I).