Algebraic Structure of Neutrosophic Duplets in Neutrosophic Rings ⟨z ∪ i⟩, ⟨Q ∪ I⟩ and ⟨R ∪ I⟩.

The concept of neutrosophy and indeterminacy I was introduced by Smarandache, to deal with neutralies. Since then the notions of neutrosophic rings, neutrosophic semigroups and other algebraic structures have been developed. Neutrosophic duplets and their properties were introduced by Florentin and other researchers have pursued this study.In this paper authors determine the neutrosophic duplets in neutrosophic rings of characteristic zero. The neutrosophic duplets of hZ <z∪i>, <Q∪I> and <R∪I> the neutrosophic ring of integers, neutrosophic ring of rationals and neutrosophic ring of reals respectively have been analysed. It is proved the collection of neutrosophic duplets happens to be infinite in number in these neutrosophic rings. Further the collection enjoys a nice algebraic structure like a neutrosophic subring, in case of the duplets collection {a-aI|a∊Z} for which 1-I acts as the neutral. For the other type of neutrosophic duplet pairs {a-aI,1-dI} where a ∊R+ and d ∊ R, this collection under component wise multiplication forms a neutrosophic semigroup. Several other interesting algebraic properties enjoyed by them are obtained in this paper. [ABSTRACT FROM AUTHOR]