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

We provide a non-commutative version of the F5 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 F5 algorithm allow to read off a basis for each Loewy layer, provided that a negativ...

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Vydáno v:Journal of symbolic computation Ročník 65; s. 111 - 129
Hlavní autor: King, Simon A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.11.2014
Témata:
[formula omitted] algorithm
Basic algebra
Loewy layer
Loewy layer
Basic algebra
F5 algorithm
ISSN:0747-7171, 1095-855X
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Shrnutí:We provide a non-commutative version of the F5 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 F5 algorithm allow to read off a basis for each Loewy layer, provided that a negative degree monomial ordering is used. As a byproduct, Gröbner bases in this setting can be computed more efficiently with the F5 algorithm than with Buchberger's algorithm.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2014.01.006