Finite Abelian algebras are fully dualizable

Wolfram Bentz (1) , Pierre Gillibert (2) , Luís Sequeira (3)

1 CEMAT - Center for Computacional and Stochastic Mathematics
2 PUCV - Pontificia Universidad Católica de Valparaíso
3 Faculdade de Ciências, Universidade de Lisboa

We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite type. We give an explicit bound on the arities of the partial and total operations appearing in the dualizing structure. In addition, we show that the enriched partial hom-clone of A is finitely generated as a clone.

Mots clés: strong duality; natural duality; dualizable algebra; Abelian algebra

Domaines: Anneaux et algèbres [math.RA]

Wolfram Bentz, Pierre Gillibert, Luís Sequeira. Finite Abelian algebras are fully dualizable. 2015. ⟨hal-01131051v2⟩