Mathematics Preprints 2001
Computational Discrete Algebra
01.32 : HEYWORTH, A. & SNELLMAN, J.
Groebner basis techniques for modules
Abstract:Standard noncommutative Groebner basis procedures are used for solving the membership problem for ideals of free noncommutative polynomial rings over fields. This paper describes Groebner basis procedures for solving the membership problem for submodules of R-modules where R is a finitely presented polynomial ring over a field.
In fact, the procedure we describe enables us to simulate computation of R-modules and may be used to construct finitely presented regular representations of modules.
Philosophically, the advantage is that computation takes place in the most free structure available. Computationally, the advantage is that with a simple application of tagging the calculations can be made by an unmodified noncommutative Groebner basis program (such as BERGMAN, SINGULAR or OPAL).