A Generalization of Gröbner Basis Algorithms to Polycyclic Group Rings

  title={A Generalization of Gr{\"o}bner Basis Algorithms to Polycyclic Group Rings},
  author={Klaus Madlener and Birgit Reinert},
  journal={J. Symb. Comput.},
It is well-known that for the integral group ring of a polycyclic group several decision problems are decidable, in particular the ideal membership problem. In this paper we define an effective reduction relation for group rings over polycyclic groups. This reduction is based on left multiplication and hence corresponds to left ideals. Using this reduction we present a generalization of Buchberger's Grobner basis method by giving an appropriate definition of “Grobner bases” in this setting and… 

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