A Lattice Formulation of the F 4 Completion Procedure

Cyrille Chenavier (1, 2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 PI.R2 - Design, study and implementation of languages for proofs and programs

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 F4 procedure. Our procedure is based on the lattice structure of reduction operators which provides 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 F4 procedure. Finally, we illustrate our procedure with a complete example.

Mots clés: Noncommutative F 4 procedure; Reduction operators; Lattice structure

Domaines: Informatique [cs]; Mathématiques [math]

Cyrille Chenavier. A Lattice Formulation of the F 4 Completion Procedure. International Journal of Algebra and Computation, 2019, 29 (1), ⟨10.1142/S0218196718500613⟩. ⟨hal-01489200v2⟩