Finite Basis for Radical Well-Mixed Difference Ideals Generated by Binomials

TL;DR

This paper proves a finite basis theorem for radical well-mixed difference ideals generated by binomials, showing that all ascending chains are finite, thus resolving a question posed by Hrushovski in the binomial context.

Contribution

It establishes the first finite basis theorem for radical well-mixed difference ideals generated by binomials, advancing the understanding of their algebraic structure.

Findings

Finite basis theorem proven for these ideals

All ascending chains of such ideals are finite

Answers a question by Hrushovski in the binomial case

Abstract

In this paper, we prove a finite basis theorem for radical well-mixed difference ideals generated by binomials. As a consequence, every strictly ascending chain of radical well-mixed difference ideals generated by binomials in a difference polynomial ring is finite, which answers a question raised by E. Hrushovski in the binomial case.