A non-commutative F-5 algorithm with an application to the computation of Loewy layers

作者：King Simon A^*

来源：Journal of Symbolic Computation, 2014, 65: 111-129.

DOI：10.1016/j.jsc.2014.01.006

• F-5 algorithm
• Basic algebra
• Loewy layer

We provide a non-commutative version of the F-5 algorithm, namely for right-modules over path algebra quotients. It terminates, if the path algebra quotient is a basic algebra. We show that the signatures used in the F-5 algorithm allow to read off a basis for each Loewy layer, provided that a negative degree monomial ordering is used. As a byproduct, Grobner bases in this setting can be computed more efficiently with the F-5 algorithm than with Buchberger%26apos;s algorithm.

• 出版日期2014-11