$t$-linked overrings of Noetherian weakly factorial domains
نویسندگان
چکیده
منابع مشابه
Intersections of valuation overrings of two-dimensional Noetherian domains
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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Let R be an integral domain with quotient field L. An overring T of R is t-linked over R if I = R implies that (T : IT ) = T for each finitely generated ideal I of R. Let Ot(R) denotes the set of all t-linked overrings of R and O(R) the set of all overrings of R. The purpose of this paper is to study some finiteness conditions on the set Ot(R). Particularly, we prove that if Ot(R) is finite, th...
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Let F be a field. We show that certain subrings contained between the polynomial ring F [X] = F [X1, · · · , Xn] and the power series ring F [X][[Y ]] = F [X1, · · · , Xn][[Y ]] have Weierstrass Factorization, which allows us to deduce both unique factorization and the Noetherian property. These intermediate subrings are obtained from elements of F [X][[Y ]] by bounding their total X-degree abo...
متن کاملNoetherian Spaces of Integrally Closed Rings with an Application to Intersections of Valuation Rings
Let H be an integral domain, and let Σ be a collection of integrally closed overrings of H. We show that if A is an overring of H such that H = ( T R∈Σ R)∩A, and if Σ is a Noetherian subspace of the space of all integrally closed overrings of H, then there exists a weakly Noetherian subspace Γ of integrally closed overrings of H such that H = ( T R∈Γ R) ∩ A, and no member of Γ can be omitted fr...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1081699-1