Algebraic Properties of Finite Neutrosophic Fields

Abstract

We explore a finite Neutrosophic field 𝑭𝒑 (𝑰) and its Neutrosophic multiplicative group 𝑭𝒑 (𝑰) × in this study. We first show |𝑭𝒑 (𝑰) ×| = (𝒑 − 𝟏) 𝟐 and then its algebraic properties are studied. The Neutrosophic Fermat's and Little Fermat's theorems over 𝑭𝒑 (𝑰) × are then proved. Finally, this paper investigates some applications of Neutrosophic Fermat's theorem over 𝑭𝒑 (𝑰) × with various illustrations.

Keywords

• neutrosophic field
• neutrosophic group
• neutrosophic fermat’s theorem
• neutrosophic little fermat’s theorem