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

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algebraAug 14, 2026Significance 8/100Registry: unreviewed

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

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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.

Source authenticatedTarizadeh's Conjecture on the Maximality of Purely-Prime Ideals →

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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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