このエントリーをはてなブックマークに追加
ID 33109
FullText URL
Author
Bagio, Dirceu
Paques, Antonio
Abstract

We deal with the following variant of the primitive element theorem: any commutative strongly separable extension of a commutative ring can be embedded in another one having primitive element. This statement holds for connected strongly separable extension of commutative rings which are either local or connected semilocal. We show that it holds for a more general family of rings, that is, for connected commutative rings whose quotient ring by the corresponding Jacobson radical is von Neumann regular and locally uniform. Some properties of the (connected) separable closure of such rings are also given as an application of this result.

Keywords
primitive element
von Neumann regular ring
locally uniform ring
strongly separable extension
separable closure
Published Date
2007-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume49
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
File Version
publisher
Refereed
True
Submission Path
mjou/vol49/iss1/11