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Algebra and Discrete Mathematics, 2009, Issue 3, Pages 20–27 (Mi adm126)  
RESEARCH ARTICLE

A variant of the primitive element theorem for separable extensions of a commutative ring

Dirceu Bagioa, Antonio Paquesb

a Departamento de Matemática, Universidade Federal de Santa Maria, 97105–900, Santa Maria, RS, Brazil
b Instituto de Matemática, Universidade Federal do Rio Grande do Sul 91509–900, Porto Alegre, RS, Brazil
Full-text PDF (210 kB)
Abstract: In this article we show that any strongly separable extension of a commutative ring $R$ can be embedded into another one having primitive element whenever every boolean localization of $R$ modulo its Jacobson radical is von Neumann regular and locally uniform.
Keywords: primitive element, separable extension, boolean localization.
Received: 12.08.2009
Revised: 25.09.2009
Bibliographic databases:
Document Type: Article
MSC: 13B05, 12F10
Language: English
Citation: Dirceu Bagio, Antonio Paques, “A variant of the primitive element theorem for separable extensions of a commutative ring”, Algebra Discrete Math., 2009, no. 3, 20–27
Citation in format AMSBIB
\Bibitem{BagPaq09}
\by Dirceu~Bagio, Antonio~Paques
\paper A variant of the primitive element theorem for separable extensions of a~commutative ring
\jour Algebra Discrete Math.
\yr 2009
\issue 3
\pages 20--27
\mathnet{http://mi.mathnet.ru/adm126}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2640385}
\zmath{https://zbmath.org/?q=an:1199.13007}
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