Proving that an analogue of Rogers’ theorem holds in Dedekind domains and finite commutative rings, indicating fundamental properties.
We prove that an analogue of Rogers’ theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals.
No takes yet. Share an insight, caveat, or question.
Petr Kucheriaviy (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: