Publicado

2014-01-01

Uniform Dimension over Skew PBW Extensions

Dimensión uniforme de las extensiones PBW torcidas

DOI:

https://doi.org/10.15446/recolma.v48n1.45196

Palabras clave:

Non-commutative rings, Filtered and graded rings, PBW extensions, Uniform dimension, Nonsingular modules (en)
Anillos no conmutativos, anillos filtrados y graduados, extensiones PBW, dimensión uniforme, módulos no singulares (es)

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Autores/as

  • Armando Reyes Universidad Nacional de Colombia
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.
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.

Referencias

A. D. Bell and K. R. Goodearl, `Uniform Rank over Differential Operator Rings and Poincaré-Birkhoff-Witt extensions', Pacific Journal of Mathematics 131, 1 (1988), 13-37.

C. Gallego and O. Lezama, `Gröbner Bases for Ideals of σ-PBW Extensions', Communications in Algebra 39, 1 (2011), 50-75.

K. R. Goodearl, Nonsingular Rings and Modules, Pure and Applied Mathematics, New York, USA, 1976.

K. R. Goodearl and T. Lenagan, `Krull Dimension of Differential Operator Rings III: Noncommutative Coeficients', Transactions of the American Mathematical Society 275, (1983), 833-859.

P. Grzeszczuk, `Goldie Dimension of Differential Operator Rings', Communications in Algebra 16, 4 (1988), 689-701.

T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, Graduate Texts in Mathematics 189, New York, USA, 1999.

A. Leroy and J. Matczuk, `Goldie Conditions for Ore Extensions over Semiprime Rings', Algebras and Representation Theory 8, (2005), 679-688.

O. Lezama and A. Reyes, `Some Homological Properties of Skew PBW Extensions', Communications in Algebra 42, (2014), 1200-1230.

J. Matczuk, `Goldie Rank of Ore Extensions', Communications in Algebra 23, (1995), 1455-1471.

J. McConnell and C. Robson, Non-commutative Noetherian Rings, with the Cooperation of L. W. Small., 2 edn, Graduate Studies in Mathematics. 30. American Mathematical Society (AMS), Providence, USA, 2001.

V. A. Mushrub, `On the Goldie Dimension of Ore Extensions with Several Variables', Fundamentalnaya i Prikladnaya Matematika 7, (2001), 1107-1121.

D. Quinn, `Embeddings of Differential Operator Rings and Goldie Dimension', Proceedings of the American Mathematical Society 102, 1 (1988), 9-16.

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

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

R. C. Shock, `Polynomial Rings over Finite-Dimensional Rings', Pacific Journal of Mathematics 42, (1972), 251-257.

G. Sigurdsson, `Differential Operator Rings whose Prime Factors have Bounded Goldie Dimension', Archiv der Mathematik (Basel) 42, (1984), 348-353.

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Cómo citar

Reyes, A. (2014). Dimensión uniforme de las extensiones PBW torcidas. Revista Colombiana De Matemáticas, 48(1), 79-96. https://doi.org/10.15446/recolma.v48n1.45196

Licencia

Derechos de autor 2014 Revista Colombiana de Matemáticas

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.