A non-commutative F5 algorithm with an application to the computation of Loewy layers
Simon A. King
TL;DR
This paper introduces a non-commutative adaptation of the F5 algorithm tailored for right-modules over path algebra quotients, enabling efficient computation of Loewy layers in specific algebraic structures.
Contribution
It develops a non-commutative F5 algorithm applicable to path algebra quotients and demonstrates its use in computing Loewy layers with negative degree monomial orderings.
Findings
Algorithm terminates for basic algebra quotients
Enables computation of Loewy layers
Applicable to non-commutative algebraic structures
Abstract
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. In addition, we use the F5 algorithm in negative degree monomial orderings to compute Loewy layers.
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