Completions of countable excellent domains and countable noncatenary domains
نویسندگان
چکیده
We find necessary and sufficient conditions for a complete local (Noetherian) ring containing the rationals to be completion of countable excellent domain. Furthermore, we noncatenary domain, as well it unique factorization
منابع مشابه
On Countable Completions of Quotient Ordered Semigroups
A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...
متن کاملThe Envelope of Holomorphy of Riemann Domains over a Countable Product of Complex Planes
This paper deals with the problem of constructing envelopes of holomorphy for Riemann domains over a locally convex space. When this locally convex space is a countable product of complex planes the existence of the envelope of holomorphy is proved and the domains of holomorphy are characterized. For the Riemann domains over the cartesian product CN of a countable number of complex planes, the ...
متن کاملCountable Ordinals
This development defines a well-ordered type of countable ordinals. It includes notions of continuous and normal functions, recursively defined functions over ordinals, least fixed-points, and derivatives. Much of ordinal arithmetic is formalized, including exponentials and logarithms. The development concludes with formalizations of Cantor Normal Form and Veblen hierarchies over normal functions.
متن کاملThe number of countable models of a countable supersimple theory
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan’s theorem on a superstable theory.
متن کاملCountable Choice and Compactness
We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p ≥ 1 (resp. p = 0), and some closed subse...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2021
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2020.09.021