References

MATRIX COMPUTATIONS ON PROJECTIVE MODULES USING NONCOMMUTATIVE GRÖBNER BASES


[1] F. Chyzak, A. Quadrat and D. Robertz, Effective algorithms for parametrizing linear control systems over ore algebras, Appl. Algebra Engrg. Comm. Comput. 16(5) (2005), 319-376.

[2] T. Cluzeau and A. Quadrat, Factoring and decomposing a class of linear functional systems, Lin. Alg. and its Appl. 428(1) (2008), 324-381.

[3] P. Cohn, Free Ideal Rings and Localizations in General Rings, Cambridge University Press, 2006.

[4] H. Fujita, Global and Krull dimensions of quantum Weyl algebras, Journal of Algebra 216(2) (1999), 405-416.

[5] C. Gallego, Matrix Methods for Projective Modules Over Extensions, Ph.D. Thesis, Universidad Nacional de Colombia, Bogotá, 2015.

[6] C. Gallego and O. Lezama, Gröbner bases for ideals of skew PBW extensions, Comm. in Algebra 39(1) (2011), 50-75.

[7] C. Gallego and O. Lezama, Matrix approach to noncommutative stably free modules and Hermite rings, Algebra and Discrete Mathematics 18(1) (2014), 110-139.

[8] C. Gallego and O. Lezama, d-Hermite rings and skew PBW extensions, São Paulo Journal of Mathematical Sciences (First online: 25 August 2015), 1-13.

[9] C. Gallego and O. Lezama, Projective modules and Gröbner 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).

[10] J. Gago-Vargas, Bases for projective modules in J. Symb. Comp. 36 (2003), 845-853.

[11] T. Y. Lam, Serre’s Problem on Projective Modules, Springer Monographs in Mathematics, Springer, 2006.

[12] T. Y. Lam, Lectures on Modules and Rings, Springer Graduate Text in Mathematics 189, 1999.

[13] O. Lezama, Matrix and Gröbner Methods in Homological Algebra over Commutative Polynomial Rings, Lambert Academic Publishing, 2011.

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

[15] A. Quadrat and D. Robertz, Computation of bases of free modules over the Weyl algebras, J. Symb. Comp. 42 (2007), 1113-1141.

[16] J. T. Stafford, Module structure of Weyl algebras, J. London Math. Soc. 18 (1978), 429-442.