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Journal Articles Journal of Pure and Applied Algebra Year : 2019

Syzygies among reduction operators

Abstract

We introduce the notion of syzygy for a set of reduction operators and relate it to the notion of syzygy for presentations of algebras. We give a method for constructing a linear basis of the space of syzygies for a set of reduction operators. We interpret these syzygies in terms of the confluence property from rewriting theory. This enables us to optimise the completion procedure for reduction operators based on a criterion for detecting useless reductions. We illustrate this criterion with an example of construction of commutative Gröbner basis.
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Dates and versions

hal-01578555 , version 1 (29-08-2017)
hal-01578555 , version 2 (09-04-2018)

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Cite

Cyrille Chenavier. Syzygies among reduction operators. Journal of Pure and Applied Algebra, 2019, ⟨10.1016/j.jpaa.2018.04.017⟩. ⟨hal-01578555v2⟩
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