Ideals on the Quantum Plane's jet space

TL;DR

This paper introduces quantum jet space rings related to the quantum plane, revealing nontrivial prime ideals and analyzing their prime spectrum to deepen understanding of quantum algebraic structures.

Contribution

It constructs quantum jet space rings with nontrivial prime ideals and provides new theorems on their prime spectrum, advancing quantum algebra research.

Findings

Existence of nontrivial prime ideals in quantum jet space rings

Theorems describing the prime spectrum of these rings

Structural insights into quantum algebraic geometry

Abstract

The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (theorems 1-4) about the prime spectrum of these rings.