Pivotal decomposition schemes inducing clones of operations

Miguel Couceiro (1) , Bruno Teheux (2)

1 ORPAILLEUR - Knowledge representation, reasonning
2 University of Luxembourg [Luxembourg]

We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of pivotally decomposable operations are clones, and show that under certain assumptions these conditions are also necessary. In the latter case, the pivotal operation together with the constant operations generate the corresponding clone.

Domaines: Anneaux et algèbres [math.RA]; Logique [math.LO]

Miguel Couceiro, Bruno Teheux. Pivotal decomposition schemes inducing clones of operations. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2018, 59 (1), pp.25-40. ⟨10.1007/s13366-017-0354-6⟩. ⟨hal-01450835⟩