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
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
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