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Noetherian domains which admit only finitely many star operations
- Authors
- Houston, Evan; Mimouni, Abdeslam; Park, Mi Hee
- Issue Date
- Sep-2012
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Noetherian domain; Star operation; Divisorial ideal
- Citation
- JOURNAL OF ALGEBRA, v.366, pp 78 - 93
- Pages
- 16
- Journal Title
- JOURNAL OF ALGEBRA
- Volume
- 366
- Start Page
- 78
- End Page
- 93
- ISSN
- 0021-8693
1090-266X
- Abstract
- In this paper, we study Noetherian domains which admit only finitely many star operations. We show that such domains (which are not fields) must have Krull dimension one, and we effectively reduce to the local case. For a one-dimensional local Noetherian domain (R, M), M nonprincipal, M-1 is an overring of R, and M-1 /M is naturally an R/M-vector space. We succeed in counting the number of star operations on R in several cases when dim(R/M) M-1 /M = 3. (C) 2012 Elsevier Inc. All rights reserved.
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