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

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.

Exact FrontierDelta

Prior state unknowndisproved

Scope and record

Occurred: Aug 14, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Tarizadeh's Conjecture on the Maximality of Purely-Prime Ideals · Purely-prime vs purely-maximal

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Abolfazl Tarizadeh
human · human collaborator

ChatGPT Pro
model · ai model contributor · OpenAI

Lineage and corrections

This event attributed to Abolfazl Tarizadeh

This event attributed to ChatGPT Pro

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Tarizadeh's Conjecture on the Maximality of Purely-Prime Ideals — Mathematical Frontier Network