Jacobson's conjecture and skew PBW
extensions

ARMANDO REYES^*

 Universidad Nacional de Colombia, Departamento de Matemáticas, Bogotá, Colombia.

Abstract. The aim of this paper is to compute the Jacobson's radical of skew PBW extensions over domains. As a consequence of this result we obtain a direct relation between these extensions and the Jacobson's conjecture, which implies that skew PBW extensions over domains satisfy this conjecture.

Keywords:Noncommutative rings, Jacobson's radical, skew PBW extensions.
MSC2010: 16N20, 16N40, 16W70, 16N60, 16S32, 16S36.

Conjetura de Jacobson y extensiones PBW torcidas

Resumen. El propósito de este artículo es calcular el radical de Jacobson de las extensiones PBW torcidas sobre dominios. Como consecuencia de este resultado obtenemos una relación directa entre estas extensiones y la conjetura de Jacobson, lo cual nos permite mostrar que las extensiones PBW torcidas sobre dominios satisfacen esta conjetura.

Palabras claves: Anillos no conmutativos, radical de Jacobson, extensiones PBW torcidas.

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^*E-mail: mareyesv@unal.edu.co.
Received: 17 April 2014, Accepted: 24 May 2014.
To cite this article: A. Reyes, Jacobson's conjecture and skew PBW extensions, Rev. Integr. Temas Mat.
32 (2014), no. 2, 139-152.