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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.54 no.1 Bogotá jan./jun. 2020

https://doi.org/10.15446/recolma.v54n1.89788 

Original articles

Minimal prime ideals of skew PBW extensions over 2-primal compatible rings

Ideales primos minimales de extensiones PBW torcidas sobre anillos compatibles 2-primal

Mohamed Louzari1  * 

Armando Reyes2 

1 Abdelmalek Essaadi University, Tetouan, Morocco

2 Universidad Nacional de Colombia, Bogotá, Colombia


Abstract:

In this paper, we characterize the units of skew PBW extensions over compatible rings. With this aim, we recall the transfer of the property of being 2-primal for these extensions. As a consequence of our treatment, the results established here generalize those corresponding for commutative rings and Ore extensions of injective type. In this way, we present new results for several noncommutative rings of polynomial type not considered before in the literature.

Keywords: Minimal prime ideal; 2-primal ring; unit; skew PBW extension

Resumen:

En este artículo, caracterizamos las unidades de las extensiones PBW torcidas sobre anillos compatibles. Con este propósito, recordamos la transferencia de la propiedad 2-primal para estas extensiones. Como una consecuencia de nuestro tratamiento, los resultados establecidos aquí generalizan aquellos correspondientes para anillos conmutativos y extensiones de Ore de tipo inyectivo. De esta manera, presentamos nuevos resultados para anillos no conmutativos de tipo polinomial no considerados antes en la literatura.

Palabras clave: Ideal primo minimal; anillo 2-primal; unidad; extensión PBW torcida

Full text available only in PDF format.

Acknowledgment.

The second named author was supported by the research fund of Faculty of Sciences, Universidad Nacional de Colombia, Sede Bogotá, Colombia, HERMES CODE 41535.

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Received: October 16, 2019; Accepted: February 11, 2020

*Correspondencia: Mohamed Louzari, Department of Mathematics, Abdelmalek Essaadi University, Tetouan, Morocco. Correo electrónico: mlouzari@yahoo.com. DOI: https://doi.org/10.15446/recolma.v54n1.89788

2010 Mathematics Subject Classification. 16N40, 16S36, 16S37, 16S38, 16S99.

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