Thirty-Third Annual Victorian Algebra Conference, Sydney, Australia, 2015

Register for: VAC33

Details of talk

TitleRemarks on Jonsson's Lemma
PresenterTomasz 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.