Arithmetic of the ring 𝐹𝑞[ε], 𝜀𝑛=0, n≥1, 𝜀𝑖+1= 𝜀𝑖, i=1,2,3

Abstract

In this memory, we will study the arithmetic operations in the quotient ring of 𝐹𝑞[x] by the polynomial xⁿ, xⁿ⁺¹=xⁿ, n=1,2,3 where 𝐹𝑞 is a finite field of order q. We will recall some basic concepts about the rings. In addition, we will present some notes over the arithmetic operations in the Ring 𝐹𝑞[e].