WHEN ARE THE PRIME IDEALS OF THE LOCALIZATION R[X](T) EXTENDED FROM R
SCIE
SCOPUS
- Title
- WHEN ARE THE PRIME IDEALS OF THE LOCALIZATION R[X](T) EXTENDED FROM R
- Authors
- Kang, BG
- Date Issued
- 2000-01
- Publisher
- UNIV HOUSTON
- Abstract
- Let R be an integrally closed integral domain, {X-alpha} a set of indeterminates over R, and T a multiplicatively closed subset of R[{X-alpha}]. We prove the equivalence of the following statements: (1) Every prime ideal of R[{X-alpha}](T) is extended from R. (2) Every ideal of R[{X-alpha}](T) is extended from R. (3) Every principal ideal of R[{X-alpha}](T) is extended from R. (4) There exists a Prufer v-multiplication overring A of R such that R[{X-alpha}](T) = A(v), where A(v) is the Kronecker function ring of A with respect to the v-operation. The case when R is not integrally closed is also taken care of. Similar statements for rings with zero divisors are considered and their equivalence is established.
- Keywords
- polynomial ring; prime ideal; localization; Prufer v-multiplication ring; Noetherian ring; ZERO DIVISORS; KRULL RINGS; DOMAINS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/21024
- ISSN
- 0362-1588
- Article Type
- Article
- Citation
- HOUSTON JOURNAL OF MATHEMATICS, vol. 26, no. 1, page. 67 - 81, 2000-01
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