A lattice formulation of the noncommutative F4 procedure

Abstract

We introduce a new procedure for constructing noncommutative Gröbner bases using a lattice formulation of completion. This leads to a lattice description of the noncommutative [Formula: see text] procedure. Our procedure is based on the lattice structure of reduction operators which provide a lattice description of the confluence property. We relate reduction operators to noncommutative Gröbner bases, we show the Diamond Lemma for reduction operators and we deduce the lattice interpretation of the [Formula: see text] procedure. Finally, we illustrate our procedure with a complete example.