Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15664912007A Generalized Primitive Element TheoremENDirceuBagioAntonioPaques<p>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.</p>
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