Details of talk
|Title||Remarks on Jonsson's Lemma|
|Presenter||Tomasz Kowalski (La Trobe University)|
|Author(s)||Dr Tomasz Kowalski|
Jonsson's Lemma is the statement that in a congruence distributive variety generated by a class K, every subdirectly irreducible algebra is a homomorphic image of a subalgebra of an ultraproduct of algebras from K. A generalised form of Jonsson's Lemma holds in congruence modular varieties: the precise statement is a little convoluted, but it implies the usual Jonsson's Lemma for congruence distributive varieties. I will present a sufficient condition, formulated in terms of congruences and the centrality relation, which implies the generalised form of the lemma. I will also show that the condition holds in certain varieties whose congruence lattices do not satisfy any nontrivial identities.