Enumeration of Neutrosophic Involutions over Finite Commutative Neutrosophic Rings

Abstract

A finite commutative ring involution is the multiplicative inverse of the element attribute R is the
element itself. This classical characteristic of a finite commutative ring makes Neutrosophic
involutions possible, which are counted, listed and assessed in this work. Assume that the
Neutrosophic ring R(I) is the finite commutative ring with unity 1 over the ring R under the
indeterminate ð‘° . We first establish some useful necessary and sufficient conditions for the
Neutrosophic components of the type ð’‚ + ð’ƒð‘° is involutory in order to understand how to count
Neutrosophic involutions of R(I). The behavior of the Neutrosophic composition table for
identifying Neutrosophic involutions and counting the number of 1s that appear on the primary
diagonal of the composition table of R(I) is also investigated in this work.