Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 1, pp. 39-66 (2016)

Gröbner bases of modules over sigma-PBW extensions

Haydee Jimenez and Oswaldo Lezama

Universidad de Sevilla and Universidad Nacional de Colombia

Abstract: For $\sigma-PWB$ extensions, we extend to modules the theory of Gröbner bases of left ideals presented in [C. Gallego and O. Lezama. Gröbner bases for ideals of sigma-PBW extensions. Comm. Algebra, 39(1):50–75, 2011.] As an application, if $A$ is a bijective quasi-commutative $\sigma-PWB$ extension, we compute the module of syzygies of a submodule of the free module $A^m$.

Keywords: PBW extensions, noncommutative Gröbner bases, Buchberger's Algorithm, module of syzygies

Classification (MSC2000): 16Z05; 18G10

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