Pure Maths Colloquium: Peter Mayr

Tarski’s finite basis problem asks for a given finite algebraic structure \(A\) whether the equational theory of \(A\) is finitely axiomatizable. More explicitely, does there exist some finite set of identities true in \(A\) that implies all identities true in \(A\)? McKenzie showed that this question is not decidable in general in 1996. Still partial results are known for many classes of algebras. I will review some of the long history of the problem, state open questions and present a recent approach on the finite basis problem for nilpotent loops.