Sobre a existencia de elemento primitivo para extensões separaveis de aneis comutativos

AUTOR(ES)

Dirceu Bagio

DATA DE PUBLICAÇÃO

2004

RESUMO

One of the classic theorems of the Galois theory of fields is the “Primitive Element Theorem”. In Galois theory of commutative rings, such a theorem does not hold, in general. In this work we give necessary and sufficient conditions for the existence of a primitive element in an strongly separable extension of a connected commutative ring. Furthermore we present a weak form of the Primitive Element Theorem and we prove that this theorem holds for strongly separable extensions of connected commutative rings whose quotient by its Jacobson radical is a von Neumann regular and locally uniform ring. We also obtain some new results about the separable closure of a connected commutative ring. In particular, we describe a relation between the separable closure of such a ring and the separable closure of each one of its residual fields.

ASSUNTO(S)

polinomios galois teoria de

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