Some Properties of the Coordinate Rings over Finite Fields

TL;DR

This paper explores properties of coordinate rings over finite fields, establishing a version of the Nullstellensatz for subsets of affine space over finite fields and discussing its applications.

Contribution

It extends the Nullstellensatz to coordinate rings over finite fields and explores its implications, which was not previously well-understood.

Findings

Nullstellensatz established for coordinate rings over finite fields

Applications of the Nullstellensatz in finite field contexts discussed

Provides foundational results for algebraic geometry over finite fields

Abstract

In this paper, we present the Nullstellensatz in case of the coordinate rings of a nonempty subset of Kn where K is a finite field Fq. Some applications of the Nullstellensatz are also discussed.