Serviços Personalizados
Journal
Artigo
Indicadores
- Citado por SciELO
- Acessos
Links relacionados
- Citado por Google
- Similares em SciELO
- Similares em Google
Compartilhar
Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.48 no.1 Bogotá jan./jun. 2014
https://doi.org/10.15446/recolma.v48n1.45196
http://dx.doi.org/10.15446/recolma.v48n1.45196
1Universidad Nacional de Colombia, Bogotá, Colombia. Email: mareyesv@unal.edu.co
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.
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.
Texto completo disponible en PDF
References
[1] 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. [ Links ]
[2] C. Gallego and O. Lezama, 'Gröbner Bases for Ideals of σ-PBW Extensions', Communications in Algebra 39, 1 (2011), 50-75.
[3] K. R. Goodearl, Nonsingular Rings and Modules, Pure and Applied Mathematics, New York, USA, [ Links ] 1976.
[4] 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. [ Links ]
[5] P. Grzeszczuk, 'Goldie Dimension of Differential Operator Rings', Communications in Algebra 16, 4 (1988), 689-701. [ Links ]
[6] T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, Graduate Texts in Mathematics 189, New York, USA, [ Links ] 1999.
[7] A. Leroy and J. Matczuk, 'Goldie Conditions for Ore Extensions over Semiprime Rings', Algebras and Representation Theory 8, (2005), 679-688. [ Links ]
[8] O. Lezama and A. Reyes, 'Some Homological Properties of Skew PBW Extensions', Communications in Algebra 42, (2014), 1200-1230. [ Links ]
[9] J. Matczuk, 'Goldie Rank of Ore Extensions', Communications in Algebra 23, (1995), 1455-1471. [ Links ]
[10] 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, [ Links ] 2001.
[11] V. A. Mushrub, 'On the Goldie Dimension of Ore Extensions with Several Variables', Fundamentalnaya i Prikladnaya Matematika 7, (2001), 1107-1121. [ Links ]
[12] D. Quinn, 'Embeddings of Differential Operator Rings and Goldie Dimension', Proceedings of the American Mathematical Society 102, 1 (1988), [ Links ] 9-16.
[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. [ Links ]
[15] R. C. Shock, 'Polynomial Rings over Finite-Dimensional Rings', Pacific Journal of Mathematics 42, (1972), 251-257. [ Links ]
[16] G. Sigurdsson, 'Differential Operator Rings whose Prime Factors have Bounded Goldie Dimension', Archiv der Mathematik (Basel) 42, (1984), 348-353. [ Links ]
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}
}