A counterexample to a question on the maximality of purely-primes

Abolfazl Tarizadeh

arXiv:2608.14251v2 Primary: math.AC Secondary: math.RA

Abstract

By using an advanced model of AI, it is proved that there exists a commutative ring having a purely-prime ideal which is not purely-maximal. This gives a counterexample to \cite[Conjecture 5.8]{Tarizadeh}.

Disclosure

“ore recently, with the advent of advanced artificial intelligence, a counterexample to this conjecture was discovered with the assistance of the AI model ChatGPT (The- orem 2.5). As anticipated in [3], a counterexample to the conjecture was expected to exist. Remarkably, the counterexample obtained here is very na”
PDF page 1

Classification: Substantial mathematical content or result generation
Multiplier: 10
Verified: 2026-08-23T05:15:24.521189Z

Structural counts

Pages 6 pdf

Theorems 1 source

Lemmas 2 source

Propositions 0 source

Corollaries 1 source

Definitions 0 source

Displayed equations 3 source

Bibliography entries 3 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Counterexample.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.