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ID 33109
フルテキストURL
著者
Bagio, Dirceu Universidade Federal de Santa Maria
Paques, Antonio Universidade Federal do Rio Grande do Sul
抄録

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.

キーワード
primitive element
von Neumann regular ring
locally uniform ring
strongly separable extension
separable closure
発行日
2007-01
出版物タイトル
Mathematical Journal of Okayama University
49巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
言語
English
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol49/iss1/11