A finite analogue of the ring of algebraic numbers

TL;DR

This paper introduces a finite analogue of the ring of algebraic numbers by constructing a quotient of the product of all finite fields of prime order, enabling new insights into linear recurrent sequences.

Contribution

It presents a novel finite analogue of the algebraic numbers ring, providing a new framework for studying linear recurrent sequences.

Findings

Established properties of the finite analogue ring.

Derived results on linear recurrent sequences using this ring.

Connected the structure to classical algebraic number theory.

Abstract

We construct an analogue of the ring of algebraic numbers, living in a quotient of the product of all finite fields of prime order. We use this ring to deduce some results about linear recurrent sequences.