2 problems

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Kainrath's conjecture on intermediate half-factorial orders
Kainrath's conjecture. Every order $\mathcal{O}'$ between a half-factorial order and $\mathcal{O}_K$ is itself half-factorial.
Conjectureopenalgebraic-number-theory half-factoriality ordersarXiv posted 2 days ago
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The overring conjecture for half-factorial orders in algebraic number fields
Overring conjecture. The overring $S$ is half-factorial.
Conjectureopenalgebraic-number-theory factorization-theory half-factorialityarXiv posted 2 days ago

Kainrath's conjecture on intermediate half-factorial orders