Star operations on overrings of Prufer domains
- Authors
- Houston, Evan; Mimouni, Abdeslam; Park, Mi Hee
- Issue Date
- 3-Aug-2017
- Publisher
- TAYLOR & FRANCIS INC
- Keywords
- Prufer domain; star operation; star regular domain
- Citation
- COMMUNICATIONS IN ALGEBRA, v.45, no.8, pp 3297 - 3309
- Pages
- 13
- Journal Title
- COMMUNICATIONS IN ALGEBRA
- Volume
- 45
- Number
- 8
- Start Page
- 3297
- End Page
- 3309
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/6185
- DOI
- 10.1080/00927872.2016.1236199
- ISSN
- 0092-7872
1532-4125
- Abstract
- Let R be a Prufer domain. We begin with two questions: (Q1) If R has only finitely many star operations, is the same true for each overring of R? and (Q2) If each proper overring of R has only finitely many star operations, is the same true for R? We show that both questions have negative answers in general, we give a complete description of when (Q1) has a positive answer (loosely, R must be almost strongly discrete), and we show that for a finite dimensional Prufer domain, the answer to (Q2) is always yes. We then study star regular Prufer domains, that is, Prufer domains R such that |Star(T)||Star(R)| for each overring T of R, and we compute the number of star operations on some particular Prufer domains.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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