DOI: http://dx.doi.org/10.18273/revint.v34n2-2016004

Armendariz property for skew PBW
extensions and their classical ring of quotients

ARMANDO REYES ^a*, HÉCTOR SUÁREZ ^b

^a Universidad Nacional de Colombia, Departamento de Matemáticas, Bogotá,
Colombia.
^b Universidad Pedagógica y Tecnológica de Colombia, Escuela de Matemáticas y
Estadística, Tunja, Colombia.

Abstract. We consider a first approach to the notion of Armendariz ring for a skew Poincaré-Birkhoff-Witt (PBW for short) extension, and its classical ring of quotients. As an immediate application of this treatment, we study the properties Baer, quasi-Baer, p.p. and p.q.-Baer rings for these extensions. In this way, we generalize several results in the literature concerning Ore extensions and skew PBW extensions.

Keywords: Armendariz, Baer, quasi-Baer, p.p. and p.q-rings, skew Poincaré-Birkhoff-Witt extensions.
MSC2010: 16D25, 16E50, 16S36.

Propiedad de Armendariz para las extensiones PBW
torcidas y su anillo clásico de cocientes

Resumen. Consideramos un primer acercamiento a la noción de anillo de Armendariz para una extensión torcida de Poincaré-Birkhoff-Witt (PBW), y su anillo clásico de cocientes. Como una aplicación inmediata de este tratamiento, estudiamos las propiedades de Baer, quasi-Baer, p.p. y p.q.-Baer para estas extensiones. De esta manera, generalizamos varios resultados de la literatura para extensiones de Ore y extensiones PBW torcidas.

Palabras clave: Armendariz, Baer, quasi-Baer, p.p. y p.q.-anillos, extensiones torcidas de Poincaré-Birkhoff-Witt.

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^*E-mail: mareyesv@unal.edu.co.
Received: 15 June 2016, Accepted: 04 August 2016.
To cite this article: A. Reyes, H. Suárez, Armendariz property for skew PBW extensions and their classical
ring of quotients, Rev. Integr. Temas Mat. 34 (2016), No. 2, 147-168.