4 papers · 1 filter
Independence algebras, basis algebras and the distributivity condition
Wolfram Bentz, Victoria Gould
Stable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that of independence algebras.…
Finite Abelian algebras are fully dualizable
Wolfram Bentz, Pierre Gillibert, Luís Sequeira
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 d…
The modularity conjecture holds for linear idempotent varieties
Wolfram Bentz, Luis Sequeira
The "Modularity Conjecture" is the assertion that the join of two nonmodular varieties is nonmodular. We establish the veracity of this conjecture for the case of linear idempotent…
Dualizability of automatic algebras
Wolfram Bentz, Brian A. Davey, Jane G. Pitkethly +1
We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizab…