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ID 53924
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Author
Yamanaka, Satoshi
Abstract
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.
Keywords
separable extension
quasi-separable extension
weakly separable extension
weakly quasi-separable extension
skew polynomial ring
derivation
Published Date
2016-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume58
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
169
End Page
182
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2016 by the Editorial Board of Mathematical Journal of Okayama University
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publisher
Refereed
True
Submission Path
mjou/vol58/iss1/9
JaLCDOI