Year: 2024
Type: article
Abstract: In this paper, we study different forms of boundness for ideals of almost Dedekind domains, generalizing the notions of critical ideals, radical factorization, and SP-domains. We show that every almost Dedekind domain has at least one non-critical maximal ideal and, indeed, the set of non-critical maximal ideals is dense in the maximal space, with respect to the constructible topology; as a consequence, we show that every almost Dedekind domain is SP-scattered, and in particular that the group Inv[Formula: see text] of invertible ideals of an almost Dedekind domain [Formula: see text] is always free. If [Formula: see text] is an almost Dedekind domain with nonzero Jacobson radical, we also show that there is at least one element whose ideal function is bounded.
Author: Dario Spirito
Institution: University of Udine
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404731279