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Mathematics Preprints 2001

Computational Discrete Algebra


Groebner basis techniques for modules


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).

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