Slender domains and compact domains
-
Christian U. Jensen
and
Anders Thorup
Abstract
We prove that a one-dimensional Noetherian domain is slender if and only if it is not a local complete ring. The latter condition for a general Noetherian domain characterizes the domains that are not algebraically compact. For a general Noetherian domain R we prove that R is algebraically compact if and only if R satisfies a condition slightly stronger than not being slender. In addition we enlarge considerably the number of classes of rings for which the question of slenderness can be answered. For instance we prove that any domain, not a field, essentially of finite type over a field is slender.
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Articles in the same Issue
- Frontmatter
- Hurewicz fibrations, almost submetries and critical points of smooth maps
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds
- Diffusion semigroup on manifolds with time-dependent metrics
- Blow-up algebras, determinantal ideals, and Dedekind–Mertens-like formulas
- A computational approach to Milnor fiber cohomology
- Metrical universality for groups
- The second and third moment of L(1/2,χ) in the hyperelliptic ensemble
- Slender domains and compact domains
- Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs
- A note on local Hardy spaces
- On the value group of a model of Peano Arithmetic
- Extremal values of the (fractional) Weinstein functional on the hyperbolic space
- Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
- Unitals in shift planes of odd order
Articles in the same Issue
- Frontmatter
- Hurewicz fibrations, almost submetries and critical points of smooth maps
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds
- Diffusion semigroup on manifolds with time-dependent metrics
- Blow-up algebras, determinantal ideals, and Dedekind–Mertens-like formulas
- A computational approach to Milnor fiber cohomology
- Metrical universality for groups
- The second and third moment of L(1/2,χ) in the hyperelliptic ensemble
- Slender domains and compact domains
- Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs
- A note on local Hardy spaces
- On the value group of a model of Peano Arithmetic
- Extremal values of the (fractional) Weinstein functional on the hyperbolic space
- Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set
- Unitals in shift planes of odd order
