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ID 53924
フルテキストURL
著者
Yamanaka, Satoshi Department of Mathematics Graduate School of Natural Science and Technology Okayama University
抄録
Separable extensions of noncommutative rings have already been studied extensively. Recently, N. Hamaguchi and A. Nakajima introduced the notions of weakly separable extensions and weakly quasiseparable extensions. They studied weakly separable polynomials and weakly quasi-separable polynomials in the case that the coefficient ring is commutative. The purpose of this paper is to give some improvements and generalizations of Hamaguchi and Nakajima's results. We shall characterize a weakly separable polynomial f(X) over a commutative ring by using its derivative f′(X) and its discriminant δ(f(X)). Further, we shall try to give necessary and sufficient conditions for weakly separable polynomials in skew polynomial rings in the case that the coefficient ring is noncommutative.
キーワード
separable extension
quasi-separable extension
weakly separable extension
weakly quasi-separable extension
skew polynomial ring
derivation
発行日
2016-01
出版物タイトル
Mathematical Journal of Okayama University
58巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
169
終了ページ
182
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
言語
English
著作権者
Copyright©2016 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol58/iss1/9