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University of Wales, Bangor - Mathematics Preprints 2001
Computational Discrete Algebra
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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).
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