Abstract
We prove that an integrally closed domain R admits only finitely many star operations if and only if R satisfies each of the following conditions: (1) R is a Prüfer domain with finite character, (2) all but finitely many maximal ideals of R are divisorial, (3) only finitely many maximal ideals of R contain a nonzero prime ideal that is contained in some other maximal ideal of R, and (4) if P ≠ (0) is the largest prime ideal contained in a (necessarily finite) collection of maximal ideals of R, then the prime spectrum of R/P is finite.
| Original language | English |
|---|---|
| Pages (from-to) | 5264-5286 |
| Number of pages | 23 |
| Journal | Communications in Algebra |
| Volume | 42 |
| Issue number | 12 |
| DOIs | |
| State | Published - Dec 2014 |
Bibliographical note
Funding Information:The third-named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0021883).
Keywords
- Conducive domain
- Prüfer domain
- Star operation
ASJC Scopus subject areas
- Algebra and Number Theory
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