On Krull rings with zero divisors
SCIE
SCOPUS
- Title
- On Krull rings with zero divisors
- Authors
- Chang, Gyu Whan; Kang, Byung Gyun
- Date Issued
- 2020-08
- Publisher
- TAYLOR & FRANCIS INC
- Abstract
- Let R be a commutative ring with identity and X-r(1) (R) the set of regular height one prime ideals of R. We will show that R is a Krull ring if and only if each regular prime ideal of R contains a t-invertible prime ideal, if and only if (1) R - boolean AND(P is an element of Xr1) ((R)) R-[P[ and it has finite character and (2) (R-[P], [P]R-[P]) is a rank one DVR for each P is an element of X-r(1) (R). It is also shown that {(R-[P], [P]R-[P]) P is an element of X-r(1) (R)} is the unique defining family for a Krull ring R.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/105581
- DOI
- 10.1080/00927872.2020.1797071
- ISSN
- 0092-7872
- Article Type
- Article
- Citation
- COMMUNICATIONS IN ALGEBRA, vol. 49, no. 1, page. 207 - 215, 2020-08
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