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Noetherian domains which admit only finitely many star operations
- Houston, Evan;
- Mimouni, Abdeslam;
- Park, Mi Hee
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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.
키워드
Noetherian domain; Star operation; Divisorial ideal; INTEGRAL-DOMAINS
- 제목
- Noetherian domains which admit only finitely many star operations
- 저자
- Houston, Evan; Mimouni, Abdeslam; Park, Mi Hee
- 발행일
- 2012-09
- 유형
- Article
- 권
- 366
- 페이지
- 78 ~ 93