Artículo

El editor solo permite decargar el artículo en su versión post-print desde el repositorio. Por favor, si usted posee dicha versión, enviela a
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we compute the stable rank of these algebras using Stafford's Stable Range Theorem and Kmax dimension. © 2018

Registro:

Documento: Artículo
Título:Stable rank of down-up algebras
Autor:Gallego, C.; Solotar, A.
Filiación:IMAS, UBA-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Down-up algebras; Kmax dimension; Krull dimension; Projective modules; Stable rank; Stably free modules
Año:2019
Volumen:526
Página de inicio:266
Página de fin:282
DOI: http://dx.doi.org/10.1016/j.jalgebra.2018.02.037
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_00218693_v526_n_p266_Gallego

Referencias:

  • Antoniou, I., Iyudu, N., Wisbauer, R., On Serre's problem for RIT algebras (2003) Comm. Algebra, 31 (12), pp. 6037-6050
  • Bavula, V., van Oystaeyen, F., Krull Dimension of generalized Weyl algebras and itered skew polynomial rings: commutative coefficients (1998) J. Algebra, 208, pp. 1-34
  • Bavula, V., Lenagan, T., Generalized Weyl algebras are tensor Krull minimal (2001) J. Algebra, 239, pp. 93-111
  • Benkart, G., Roby, T., Down-up algebras (1998) J. Algebra, 209, pp. 305-344
  • Carvalho, P., Musson, I., Down-up algebras and their representation theory (2000) J. Algebra, 228, pp. 286-310
  • Carvalho, P., Musson, I., Monolithic modules over Noetherian rings (2011) Glasg. Math. J., 53, pp. 683-692
  • Chouhy, S., Herscovich, E., Solotar, A., Hochschild homology and cohomology of down-up algebras (2018) J. Algebra, 498, pp. 102-128
  • Iyudu, N., Wisbauer, R., Non-trivial stably free modules over crossed products (2009) J. Phys. A, 42, pp. 1-11
  • Jordan, D.A., Down-up algebras and ambiskew polynomial rings (2000) J. Algebra, 228, pp. 311-346
  • Kirkman, R., Musson, I., Passman, D., Noetherian down-up algebras (1999) Proc. Amer. Math. Soc., 127 (11), pp. 3161-3167
  • Lam, T.Y., Serre's Problem on Projective Modules (2006) Springer Monogr. Math., , Springer
  • Lam, T.Y., A crash course on stable range, cancellation, substitution, and exchange (2004) J. Algebra Appl., 3 (3), pp. 301-343
  • McConnell, J., Robson, J., Noncommutative Noetherian Rings (2001) Grad. Stud. Math., 30. , AMS
  • Stafford, J.T., Module structure of Weyl algebras (1978) J. Lond. Math. Soc., 18, pp. 429-442
  • Stafford, J.T., On the stable range of right noetherian rings (1981) Bull. Lond. Math. Soc., 13, pp. 39-41
  • Stafford, J.T., Stable free, projective right ideals (1985) Compos. Math., 54, pp. 63-78
  • Stafford, J.T., Absolute stable rank and quadratic forms over noncommutative rings (1990) K-Theory, 4, pp. 121-130
  • Suslin, A.A., The cancellation problem for projective modules and related topics (1979) Ring Theory, Proc. Conf., Univ. Waterloo, Waterloo, 1978, Lecture Notes in Math., 734, pp. 323-338. , Springer-Verlag New York–Berlin
  • Tintera, G., Kmax and stable rank of enveloping algebras (1993) Proc. Amer. Math. Soc., 119 (3), pp. 691-696
  • Zhao, K., Centers of down-up algebras (1999) J. Algebra, 214, pp. 103-121

Citas:

---------- APA ----------
Gallego, C. & Solotar, A. (2019) . Stable rank of down-up algebras. Journal of Algebra, 526, 266-282.
http://dx.doi.org/10.1016/j.jalgebra.2018.02.037
---------- CHICAGO ----------
Gallego, C., Solotar, A. "Stable rank of down-up algebras" . Journal of Algebra 526 (2019) : 266-282.
http://dx.doi.org/10.1016/j.jalgebra.2018.02.037
---------- MLA ----------
Gallego, C., Solotar, A. "Stable rank of down-up algebras" . Journal of Algebra, vol. 526, 2019, pp. 266-282.
http://dx.doi.org/10.1016/j.jalgebra.2018.02.037
---------- VANCOUVER ----------
Gallego, C., Solotar, A. Stable rank of down-up algebras. J. Algebra. 2019;526:266-282.
http://dx.doi.org/10.1016/j.jalgebra.2018.02.037