DIMENSIONAL GROUPS AND FIELDS

被引：4
|
作者：
Wagner, Frank O. [1 ]
机构：
[1] Univ Lyon 1, CNRS, Inst Camille Jordan UMR 5208, 21 Ave Claude Bernard, F-69622 Villeurbanne, France
来源：
JOURNAL OF SYMBOLIC LOGIC | 2020年 / 85卷 / 03期
关键词：
dimension; chain condition; group; domain; skew field; definability; pseudofinite group of small dimension;
D O I：
10.1017/jsl.2020.48
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite (m) over tilde (c)-group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.
引用
收藏
页码：918 / 936
页数：19
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