Noncommutative involutive bases
نویسنده
چکیده
Gröbner Basis theory originated in the work of Buchberger [4] and is now considered to be one of the most important and useful areas of computer algebra. In 1993, Zharkov and Blinkov [13] proposed an alternative method of computing a commutative Gröbner Basis, namely the computation of an Involutive Basis. In the mid 1980’s, Mora showed [11] that Buchberger’s work could be generalised for noncommutative rings. This article explores the issues surrounding the corresponding generalisation for Involutive Bases, and constructs a noncommutative involutive division which, when used with the noncommutative involutive basis algorithm, returns a noncommutative Gröbner Basis on termination.
منابع مشابه
On Noncommutative Involutive Divisions
Buchberger’s algorithm for computing a Gröbner basis solves the ideal membership problem over commutative polynomial rings. In the early 1990’s, an alternative to this algorithm was found, namely the involutive basis algorithm, which provides a Gröbner basis with extra combinatorial properties. Buchberger’s work was generalised to noncommutative polynomial rings by Bergman and Mora during the 1...
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