Analysis of G-Dedekind domains demonstrates that every projective ideal is principal in indeterminate fields, indicating significant properties of these domains.
Let [Formula: see text] be an extension of domains, [Formula: see text] be an indeterminate over [Formula: see text]. Let [Formula: see text] be a fixed integer such that [Formula: see text] and [Formula: see text]. We prove that [Formula: see text] is a [Formula: see text]-Dedekind domain (NWF domain) if and only if both [Formula: see text] and [Formula: see text] are fields and [Formula: see text]. We also show that if [Formula: see text] is a [Formula: see text]-Dedekind domain, then every projective ideal of [Formula: see text] is principal.
No takes yet. Share an insight, caveat, or question.
Hu et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: