Abstract
In this paper, we investigate the linkage of ideals, in Noetherian and non-Noetherian settings, with the aim to establish new characterizations of classical notions of domains through linkage theory. Two main results assert that a Noetherian domain is Dedekind if and only if it has the primary linkage property; and a domain is almost Dedekind (resp., Prüfer) if and only if it has the linkage (resp., finite linkage) property. Also, we prove that a finite-dimensional valuation domain is a DVR (i.e., Noetherian) if and only if it has the primary linkage property.
| Original language | English |
|---|---|
| Pages (from-to) | 799-809 |
| Number of pages | 11 |
| Journal | Algebras and Representation Theory |
| Volume | 24 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 2021 |
Bibliographical note
Publisher Copyright:© 2020, Springer Nature B.V.
Keywords
- Almost Dedekind domain
- Dedekind domain
- Divisoriality
- Invertibility
- Linkage
- Noetherian domain
- Prüfer domain
- Valuation domain
ASJC Scopus subject areas
- General Mathematics
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