SciELO - Scientific Electronic Library Online

vol.50 issue1A Refinement and a divided difference reverse of Jensen's inequality with applicationsOn the well-posedness for the Chen-Lee equation in periodic Sobolev spaces author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google


Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.50 no.1 Bogotá Jan. 2016 


Filtered-graded transfer of noncommutative Gröbner bases

Transferencia filtrado-graduado de bases de Gröbner no conmutativas

Claudia Gallego1

1 Universidad Nacional de Colombia, Bogotá, Colombia


As the case of free k-algebras and PBW algebras, given a bijective skew PBW extension A, we will show that it is possible transfer Gröbner bases between A and its associated graded ring.

Keywords: Noncommutative Gröbner bases; skew PBW extensions; filtered module; graded module.

2010 Mathematics Subject Classification: Primary: 16Z05. Secondary: 16W70, 16W50.


Como en el caso de k-álgebras libres y PBW álgebras, dada A una extensión PBW torcida biyectiva, mostraremos que es posible transferir bases de Gröbner entre A y su anillo graduado asociado.

Palabras claves: Bases de Gröbner no conmutativas; extensiones PBW torcidas; módulo filtrado; módulo graduado.

Texto completo disponible en PDF


[1] Gómez-Torrecillas J. Bueso, J. and A. Verschoren, Algorithmic Methods in noncommutative Algebra: Applications to Quantum Groups, Kluwer, 2003.         [ Links ]

[2] C. Gallego, Matrix methods for projective modules over sigma-PBW extensions, Tesis doctoral, Universidad Nacional de Colombia, Bogotá, 2015.         [ Links ]

[3] C. Gallego and O. Lezama, Projective modules and Gróbner bases for skew PBW extensions, to appear in "Algebraic and Symbolic Computation Methods in Dynamical Systems" in the Springer series "Advances in Delays and Dynamics"         [ Links ].

[4] _______, Gröbner bases for ideals of skew PBW extensions, Communications in Algebra 39 (2011), no. 1, 50-75.         [ Links ]

[5] H. Jiménez and O. Lezama, Gröbner bases for modules over sigma-PBW extensions, Acta Mathematica Academiae Paedagogicae Nyíregyháziensis 31 (2015), no. 3.         [ Links ]

[6] O. Lezama and M. Paiba, Computing finite presentations of Tor and Ext over skew PBW extensions and some applications, arXiv:1510.03446 [math.RA]         [ Links ].

[7] O. Lezama and M. Reyes, Some homological properties of skew PBW extensions, Communications in Algebra 42 (2014), 1200-1230.         [ Links ]

[8] H. Li, Noncommutative Gröbner Bases and Filtered-Graded Transfer, Lecture Notes in Mathematics, Vol. 1795, Springer, 2002.         [ Links ]

[9] C. Nastasescu and F. Van Oystaeyen, Graded and filtered rings and modules, Springer, 1979.         [ Links ]

(Recibido: enero de 2016 Aceptado: febrero de 2015)

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License