Uniform Dimension over Skew PBW Extensions

Dimensión uniforme de las extensiones PBW torcidas

ARMANDO REYES1

1Universidad Nacional de Colombia, Bogotá, Colombia. Email: mareyesv@unal.edu.co

Abstract

The aim of the present paper is to show that, under some conditions, the uniform dimension of a ring R is the same as the uniform dimension of a skew Poincaré-Birkhoff-Witt extension built on R.

Key words: Non-commutative rings, Filtered and graded rings, PBW extensions, Uniform dimension, Nonsingular modules.

2000 Mathematics Subject Classification: 16P40, 16P60, 16W70, 13N10, 16S36.

Resumen

El propósito de este artículo es mostrar que bajo ciertas condiciones, la dimensión uniforme de un anillo R coincide con la dimensión uniforme de una extensión Poincaré-Birkhoff-Witt torcida de R.

Palabras clave: Anillos no conmutativos, anillos filtrados y graduados, extensiones PBW, dimensión uniforme, módulos no singulares.

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References

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[13] A. Reyes, Ring and Module Theoretic Properties of σ-PBW Extensions, Ph.D. Thesis, Universidad Nacional de Colombia, 2013a.

[14] A. Reyes, `Gelfand-Kirillov Dimension of Skew PBW Extensions', Revista Colombiana de Matemáticas 47, 1 (2013b), 95-111.

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(Recibido en julio de 2013. Aceptado en enero de 2014)

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCMv48n1a05,
    AUTHOR  = {Reyes, Armando},
    TITLE   = {{Uniform Dimension over Skew \boldsymbol{PBW} Extensions}},
    JOURNAL = {Revista Colombiana de Matemáticas},
    YEAR    = {2014},
    volume  = {48},
    number  = {1},
    pages   = {79--96}
}