Abstract
The author and Ira J. Papick have termed an integral domain R a going-down ring if R ⊂ T satisfies going-down for each domain T containing R. The present paper investigates conditions which, for an integral extension A ⊂ B of domains, imply that A (respectively B ) is going-down whenever B (respectively A ) is going-down. This explains the “descent” (respectively “ascent”) in the title. Two typical results (the first about descent, the second about ascent) are given next.
Publisher
Cambridge University Press (CUP)
Reference20 articles.
1. Beiträge zur Arithmetik kommutativer Integritätsbereiche. III: Zum Dimensionsbegriff der Idealtheorie;Krull;Math. Z.,1936
2. On Groups of Order p
α
q
β
3. Topologically defined classes of going-down domains
4. The spectrum of a ring as a partially ordered set
5. Untersuchungen über Teilbarkeitseigenschaften in Kürpern;Prüfer;J. reine angew. Math.,1932
Cited by
16 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On almost valuation ring pairs;Journal of Algebra and Its Applications;2020-07-15
2. CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS;International Electronic Journal of Algebra;2014-12-01
3. ON SEMINORMAL INTEGRAL DOMAINS WITH TREED OVERRINGS;International Electronic Journal of Algebra;2014-06-01
4. Pairs of Domains Where All Intermediate Domains are Treed;Arabian Journal for Science and Engineering;2011-09-15
5. VALUATIVE DOMAINS;Journal of Algebra and Its Applications;2010-02