ON DERIVED GROUPS OF DIVISION RINGS .2.

被引：13

作者：

MAHDAVIHEZAVEHI, M

AKBARIFEYZAABAADI, S

MEHRAABAADI, M

HAJIABOLHASSAN, H

机构：

[1] Department of Mathematical Sciences, Sharif University of Technology, 11365-9415, Tehran

来源：

COMMUNICATIONS IN ALGEBRA | 1995年 / 23卷 / 08期

关键词：

D O I：

10.1080/00927879508825374

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let D be a division ring with centre F and denote by D' the derived group (commutator subgroup) of D* = D - {O}. It is shown that if each element of D' is algebraic over F, then D is algebraic over F. It is also proved that each finite separable extension of F in D is of the form F(c) for some element c in the derived group D'. Using these results, It is shown that if each element of the derived group D' is of bounded degree over F, then D is finite dimensional over F.

引用

页码：2881 / 2887

页数：7