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Tarizadeh's Conjecture on the Maximality of Purely-Prime Ideals

Algebra · posed by Abolfazl Tarizadeh · disproved

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Statement

Every purely-maximal ideal of a commutative ring is purely-prime, and the converse holds for several important classes of rings; Tarizadeh conjectured (Conjecture 5.8 of his earlier published paper) that in a commutative ring every purely-prime ideal is purely-maximal. False: there is a commutative ring with a purely-prime ideal that is not purely-maximal.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    ChatGPT Pro, with Abolfazl Tarizadeh

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    In the author's words: after years without progress on his own conjecture, "by using an advanced model of AI (ChatGPT Pro), a counterexample is found to this conjecture". The counterexample is the paper's content; the conjecture's own poser credits the model with finding it.

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