# Algebra Seminar talk

2018-11-09 (10:15)

Miroslav **Olšák** (Charles University Prague)*Loop conditions*

Abstract:

It is already known that for a locally finite variety, having
a Taylor term, having a term satisfying s(r,a,r,e)=s(a,r,e,a), and
having a term s(x,x,y,y,z,z)=s(y,z,z,x,x,y) are equivalent conditions.
On the other hand, there is an infinite idempotent Taylor algebra
without any term satisfying a non-trivial linear condition. Such
conditions correspond to a property certain graphs are forced to have
loops, we call them loop conditions. We will discuss relative strength
between loop conditions and consequences of the results.