Algebra Seminar talk
Miroslav Olšák (Charles University Prague)
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.