An analogue of Rogers' theorem on sieving in commutative rings

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.

4 pages. Corrected the proof of Lemma 1 (the statement is unchanged); other minor revisions