3 problems

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The hereditary atomicity conjecture for integral domains
Hereditary atomicity conjecture. Every hereditarily atomic domain satisfies the ACCP.
Conjecturerefutedatomicity commutative-algebra integral-domainsarXiv posted 2 days ago
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Gotti's atomicity-ascent conjecture for exponentially cyclic monoids
An exponentially cyclic monoid is a Puiseux monoid in the class studied by Gotti; for such a monoid $M$ , consider its monoid algebra $\mathbb{Q}[M]$ over the field of rationals. Go…
Conjectureopenatomicity commutative-algebra monoid-algebrasarXiv posted 2 days ago
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Gotti's atomicity-ascent conjecture for exponentially cyclic Puiseux monoids
Let $q$ belong to the set … and let $M_q$ be the exponentially cyclic Puiseux monoid associated to $q$ . Gotti's atomicity-ascent conjecture. If $M_q$ is atomic, then its monoid alg…
Conjectureopenatomicity commutative-algebra monoid-algebrasarXiv posted 2 days ago

The hereditary atomicity conjecture for integral domains