Theory on Duplicity of Finite Neutrosophic Rings

Abstract

This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic
rings. The authors establish duplex ring
Dup R( )
and neutrosophic duplex ring
Dup R I   
by way of various
illustrations. The tables of different duplicities are constructed to reveal the comparison between rings
Dup Z n  , Dup Dup Z   n 
and
Dup Dup Dup Z    n 
for the cyclic ring
Z
n
. The proposed duplicity
structures have several algebraic systems with dissimilar consequences. Author’s characterize finite rings with
R R
is different from the duplex ring
Dup R 
. However, this characterization supports that
R R Dup R    
for some well known rings, namely zero rings and finite fields.