INTEGRALLY CLOSED DOMAINS WITH ONLY FINITELY MANY STAR OPERATIONS
- Authors
- Houston, Evan; Mimouni, Abdeslam; Park, Mi Hee
- Issue Date
- Dec-2014
- Publisher
- TAYLOR & FRANCIS INC
- Keywords
- Conducive domain; Prufer domain; Star operation
- Citation
- COMMUNICATIONS IN ALGEBRA, v.42, no.12, pp 5264 - 5286
- Pages
- 23
- Journal Title
- COMMUNICATIONS IN ALGEBRA
- Volume
- 42
- Number
- 12
- Start Page
- 5264
- End Page
- 5286
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/13961
- DOI
- 10.1080/00927872.2013.837477
- ISSN
- 0092-7872
1532-4125
- 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 Prufer 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 not equal (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.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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