Monomial Orderings, Rewriting Systems, and Gröbner Bases for the Commutator Ideal of a Free Algebra
نویسندگان
چکیده
منابع مشابه
Monomial Orderings, Rewriting Systems, and Gröbner Bases for the Commutator Ideal of a Free Algebra
In this paper we consider a free associative algebra on three generators over an arbitrary field K. Given a term ordering on the commutative polynomial ring on three variables over K, we construct uncountably many liftings of this term ordering to a monomial ordering on the free associative algebra. These monomial orderings are total well orderings on the set of monomials, resulting in a set of...
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Let I denote the commutator ideal in the free associative algebra on m variables over an arbitrary field. In this article we prove there are exactly m! finite Gröbner bases for I , and uncountably many infinite Gröbner bases for I with respect to total division orderings. In addition, for m = 3 we give a complete description of its universal Gröbner basis. Let A be a finite set and let K be a f...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1999
ISSN: 0747-7171
DOI: 10.1006/jsco.1998.0245