The completion and Krull's generalized principal ideal theorem on r-Noetherian rings
SCIE
SCOPUS
- Title
- The completion and Krull's generalized principal ideal theorem on r-Noetherian rings
- Authors
- Chang, Gyu Whan; Kang, Byung Gyun
- Date Issued
- 2018-03
- Publisher
- TAYLOR & FRANCIS INC
- Abstract
- A ring is called an r-Noetherian ring if every regular ideal is finitely generated. Let R be an r-Noetherian ring, let / be a regular ideal of R, and let (R)over-cap be the I-adic completion of R. We show that (R)over-cap is a Noetherian ring and dim(R)over-cap = sup {r-ht(M) vertical bar M is an element of Max(R) and I subset of M}. Let P be a prime ideal of R. We also prove that for any a is an element of reg(P), r-htP = ht(P/aR) + 1 and that if P is minimal over an n-generated regular ideal, then r-htP <= n.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/95935
- DOI
- 10.1080/00927872.2017.1350698
- ISSN
- 0092-7872
- Article Type
- Article
- Citation
- COMMUNICATIONS IN ALGEBRA, vol. 46, no. 3, page. 1231 - 1236, 2018-03
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