ID | 33109 |
FullText URL | |
Author |
Bagio, Dirceu
Paques, Antonio
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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
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Published Date | 2007-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume49
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 171
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End Page | 181
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol49/iss1/11
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JaLCDOI |