Year: 2025
Type: article
Abstract: We study the freeness of the group $$\textrm{Inv}(D)$$ Inv ( D ) of invertible ideals of an integral domain D , and the freeness of some related groups of (fractional) ideals. We study the relation between $$\textrm{Inv}(D)$$ Inv ( D ) and $$\textrm{Inv}(D_P)$$ Inv ( D P ) , in particular in the locally finite case, and we analyze in more detail the case where D is Noetherian (obtaining a characterization of when $$\textrm{Inv}(D)$$ Inv ( D ) is free for one-dimensional analytically unramified Noetherian domains) and where D is Prüfer.
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: hybrid
Estimated APC paid: $3,390
Funder: Università degli Studi di Udine
OpenAlex ID: W4416028802