Gröbner bases for modules
J Bueso, J Gómez-Torrecillas, A Verschoren… - Algorithmic Methods in …, 2003 - Springer
J Bueso, J Gómez-Torrecillas, A Verschoren, J Bueso, J Gómez-Torrecillas, A Verschoren
Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups, 2003•SpringerUntil now, we have only dealt with ideals of PBW rings and shown how Gröbner bases may
efficiently be used to solve classical questions like the membership or equality problem. In
the present chapter we will generalize this approach and show how it applies as well to
submodules of the free module R n Actually, it appears that this set-up may also be used to
calculate syzygy modules, both in the ideal and (more generally) the module case. The
introduction and study of Gröbner bases themselves depends heavily upon the use of …
efficiently be used to solve classical questions like the membership or equality problem. In
the present chapter we will generalize this approach and show how it applies as well to
submodules of the free module R n Actually, it appears that this set-up may also be used to
calculate syzygy modules, both in the ideal and (more generally) the module case. The
introduction and study of Gröbner bases themselves depends heavily upon the use of …
Abstract
Until now, we have only dealt with ideals of PBW rings and shown how Gröbner bases may efficiently be used to solve classical questions like the membership or equality problem. In the present chapter we will generalize this approach and show how it applies as well to submodules of the free module R n Actually, it appears that this set-up may also be used to calculate syzygy modules, both in the ideal and (more generally) the module case. The introduction and study of Gröbner bases themselves depends heavily upon the use of admissible orders on a notion which generalizes the homonymous one over ℕ n and which possesses similar properties. On the other hand, it should also be clear that an analogue of the division algorithm for modules will play a leading role throughout.
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