A non-commutative F5 algorithm with an application to the computation of Loewy layers

被引：1
|
作者：
King, Simon A. [1 ]
机构：
[1] Univ Jena, Inst Math, Dept Math & Comp Sci, D-07745 Jena, Germany
来源：
JOURNAL OF SYMBOLIC COMPUTATION | 2014年 / 65卷
关键词：
F-5; algorithm; Basic algebra; Loewy layer; GROBNER BASES;
D O I：
10.1016/j.jsc.2014.01.006
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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's algorithm. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：111 / 129
页数：19
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