Pairs of Domains Where all Intermediate Domains are Noetherian
نویسندگان
چکیده
منابع مشابه
On Matlis domains and Prüfer sections of Noetherian domains
The class of Matlis domain, those integral domains whose quotient field has projective dimension 1, is surprisingly broad. However, whether every domain of Krull dimension 1 is a Matlis domain does not appear to have been resolved in the literature. In this note we construct a class of examples of one-dimensional domains (in fact, almost Dedekind domains) that are overrings of K[X, Y ] but are ...
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We survey and extend recent work on integrally closed overrings of two-dimensional Noetherian domains, where such overrings are viewed as intersections of valuation overrings. Of particular interest are the cases where the domain can be represented uniquely by an irredundant intersection of valuation rings, and when the valuation rings can be chosen from a Noetherian subspace of the Zariski-Rie...
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We determine the relationship between the cardinality of a Noetherian integral domain and the cardinality of a residue field. One consequence of the main result is that it is provable in ZFC that there is a Noetherian domain of cardinality א1 with a finite residue field, but the statement “There is a Noetherian domain of cardinality א2 with a finite residue field” is equivalent to the negation ...
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In this paper all coordinates in two variables over a Noetherian Q-domain of Krull dimension one are proved to be projectively tame. In order to do this, some results concerning projectively-tameness of polynomials in general are shown. Furthermore, we deduce that all automorphisms in two variables over a Noetherian reduced ring of dimension zero are tame.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.2307/1996725