Dirceu Bagio, Antonio Paques, “A variant of the primitive element theorem for separable extensions of a commutative ring”, Algebra Discrete Math., 2009, Issue 3,Pages <nobr>20

RESEARCH ARTICLE

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

Dirceu Bagio^a, Antonio Paques^b

^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

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.

MSC: 13B05, 12F10

Received: 12.08.2009
Revised: 25.09.2009

Language: English