GALOIS SUBFIELDS OF TAME DIVISION ALGEBRAS

被引：3

作者：

Hanke, Timo ^{[1
]}

Neftin, Danny ^{[2
]}

Wadsworth, Adrian ^{[3
]}

机构：

[1] Rhein Westfal TH Aachen, Lehrstuhl Math D, Pontdriesch 14-16, D-52062 Aachen, Germany

[2] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA

[3] Univ Calif San Diego, Dept Math, 9500 Gilman Dr, La Jolla, CA 92093 USA

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2016年 / 211卷 / 01期

基金：

美国国家科学基金会;

关键词：

NONCROSSED PRODUCTS;

D O I：

10.1007/s11856-015-1275-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a finite-dimensional tame division algebra D over a Henselian field F has a maximal subfield Galois over F if and only if its residue division algebra (D) over bar has a maximal subfield Galois over the residue field (F) over bar. This generalizes the mechanism behind several known noncrossed product constructions to a crossed product criterion for all tame division algebras, and in particular for all division algebras if the residue characteristic is 0. If (F) over bar is a global field, the criterion leads to a description of the location of noncrossed products among tame division algebras, and their discovery in new parts of the Brauer group.

引用

页码：367 / 389

页数：23

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