منابع مشابه
Cardinalities of Residue Fields of Noetherian Integral Domains
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 ...
متن کاملNon-noetherian Grothendieck Duality
For any separated map f : X → Y of quasi-compact quasiseparated schemes, Rf∗ : D + qc(X) → D (Y ) has a right adjoint f . If f is proper and pseudo-coherent (e.g., finitely-presented and flat) then Duality and tor-independent Base Change hold for f . Preface This is a research summary written early in 1991, concerning results obtained by the author during a stay at MSRI in Berkeley during 1989–...
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Notations and conventions 296 Introduction 296 I. Serre duality and almost split sequences 300 I.1. Preliminaries on Serre duality 300 I.2. Connection between Serre duality and Auslander–Reiten triangles 304 I.3. Serre functors on hereditary abelian categories 307 II. Hereditary noetherian abelian categories with non-zero projective objects 309 II.1. Hereditary abelian categories constructed fr...
متن کاملOn the Existence of Minimal Realizations of Linear Dynamical Systems over Noetherian Integral Domains
This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions ca...
متن کاملOn 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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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1999
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181071650