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

页码：918 / 936

页数：19

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