Abstract
In this paper, we give complete characterizations of Noetherian domains and integrally closed domains in which every ideal is projectively equivalent to a prime ideal. We also characterize pullbacks satisfying this property and show how to construct integral domains in which every ideal is projectively equivalent to a prime ideal outside the context of Noetherian domains and integrally closed domains.
| Original language | English |
|---|---|
| Pages (from-to) | 119-141 |
| Number of pages | 23 |
| Journal | Journal of Commutative Algebra |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2017 |
Bibliographical note
Publisher Copyright:© 2017 Rocky Mountain Mathematics Consortium.
Keywords
- Class group
- Dedekind domain
- Integral closure of ideals
- Projectively equivalent ideals
- Prüfer domain
- Pullbacks
ASJC Scopus subject areas
- Algebra and Number Theory
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