منابع مشابه
Algebraically compact functors
In a previous paper, we investigated the relation between the initial algebra and terminal coalgebra for an endofunctor on the category of sets. In this one we study conditions on a functor to be algebraically compact, which means that the canonical comparison morphism between those objects is an isomorphism. Introduction Suppose C is a category and T : C −→ C is a functor. In both [Barr, 1991]...
متن کاملPseudo Algebraically Closed Fields over Rings
We prove that for almost all σ ∈ G(Q)e the field Q̃(σ) has the following property: For each absolutely irreducible affine variety V of dimension r and each dominating separable rational map φ: V → Ar there exists a point a ∈ V (Q̃(σ)) such that φ(a) ∈ Zr. We then say that Q̃(σ) is PAC over Z. This is a stronger property then being PAC. Indeed we show that beside the fields Q̃(σ) other fields which ...
متن کاملLocally Compact Baer Rings
Locally direct sums [W, Definition 3.15] appeared naturally in classification results for topological rings (see, e.g.,[K2], [S1], [S2], [S3], [U1]). We give here a result (Theorem 3) for locally compact Baer rings by using of locally direct sums. 1. Conventions and definitions All topological rings are assumed associative and Hausdorff. The subring generated by a subset A of a ring R is denote...
متن کاملCompact Sets of Functions and Function Rings
A widely used theorem of analysis asserts that a uniformly bounded, equicontinuous family of functions has a compact closure in the space of continuous functions. This lemma, variously attributed to Arzela, Escoli, Montel, Vitali, and so on, is of importance in the theory of integral equations, conformal mapping, calculus of variations, and so on. In recent years the lemma has been generalized ...
متن کاملThe classification of algebraically closed alternative division rings of finite central dimension
A classical result of Noncommutative Algebra due to I. Niven, N. Jacobson and R. Baer asserts that an associative noncommutative division ring D has finite dimension over its center R and is algebraically closed (that is, every nonconstant polynomial in one indeterminate with left, or right, coefficients in D has a root in D) if and only if R is a real closed field and D is isomorphic to the ri...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2014
ISSN: 0166-8641
DOI: 10.1016/j.topol.2014.08.004