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On the Finiteness of Gröbner Bases Computation in Quotients of the Free Algebra

  • Patrik Nordbeck

Abstract.

We investigate, for quotients of the non-commutative polynomial ring, a property that implies finiteness of Gröbner bases computation, and examine its connection with Noetherianity. We propose a Gröbner bases theory for our factor algebras, of particular interest for one-sided ideals, and show a few applications, e.g. how to compute (one-sided) syzygy modules.

Keywords: Non-commutative algebras, Gröbner bases, Dickson's lemma, Noetherianity, Syzygies. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Patrik Nordbeck
    • 1
  1. 1.Lund University, Centre for Mathematical Sciences, Box 118, 221 00 Lund, Sweden (e-mail: nordbeck@maths.lth.se)SE

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