ON KRULL OVERRINGS OF A MAROT RING WHOSE REGULAR IDEALS ARE FINITELY GENERATED
SCIE
SCOPUS
- Title
- ON KRULL OVERRINGS OF A MAROT RING WHOSE REGULAR IDEALS ARE FINITELY GENERATED
- Authors
- Chang, GW; Kang, BG
- Date Issued
- 2000-01
- Publisher
- MARCEL DEKKER INC
- Abstract
- Let R be a Marot ring whose regular ideals are finitely generated and D a Krull overring of R. In this paper, we show that if reg-dimR less than or equal to 2, then each regular ideal of D is finitely generated and reg-dimD less than or equal to 2. In particular, each regular ideal of a Krull overring of a Noetherian ring R is finitely generated provided that (regular) Krull-dimension R less than or equal to 2. This is a generalization of the well-known fact that a Krull overring of a Noetherian domain with Krull-dimension less than or equal to 2 is also a Noetherian domain with Krull-dimension less than or equal to 2.
- Keywords
- INTEGRAL CLOSURE; ZERO DIVISORS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21035
- DOI
- 10.1080/00927870008826976
- ISSN
- 0092-7872
- Article Type
- Article
- Citation
- COMMUNICATIONS IN ALGEBRA, vol. 28, no. 5, page. 2533 - 2542, 2000-01
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