An analogue of Rogers' theorem on sieving in commutative rings
Commutative Algebra
2026-05-05 v2 Number Theory
Abstract
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.
Cite
@article{arxiv.2603.14080,
title = {An analogue of Rogers' theorem on sieving in commutative rings},
author = {Petr Kucheriaviy},
journal= {arXiv preprint arXiv:2603.14080},
year = {2026}
}
Comments
4 pages. Corrected the proof of Lemma 1 (the statement is unchanged); other minor revisions