On the finiteness of Gröbner bases computation in quotients of the free algebra
Nordbeck, Patrik (2001). On the finiteness of Gröbner bases computation in quotients of the free algebra. Applicable Algebra in Engineering, Communication and Computing, 11, (3), 157 - 180
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Published
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English
Authors:
Nordbeck, Patrik
Department:
Mathematics (Faculty of Engineering)
Algebra
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 ;
Grobner bases ;
Dickson's lemma ;
Noetherianity ;
syzygies ;
POLYNOMIAL-RINGS
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