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
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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.
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キーワード | separable extension
quasi-separable extension
weakly separable extension
weakly quasi-separable extension
skew polynomial ring
derivation
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発行日 | 2016-01
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出版物タイトル |
Mathematical Journal of Okayama University
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巻 | 58巻
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号 | 1号
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出版者 | Department of Mathematics, Faculty of Science, Okayama University
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開始ページ | 169
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終了ページ | 182
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ISSN | 0030-1566
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NCID | AA00723502
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資料タイプ |
学術雑誌論文
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言語 |
英語
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著作権者 | Copyright©2016 by the Editorial Board of Mathematical Journal of Okayama University
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論文のバージョン | publisher
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査読 |
有り
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Submission Path | mjou/vol58/iss1/9
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JaLCDOI |