Petr Vojtechovsky – Propagating equations with an application to Moufang theorem

University of Denver

An equation $t$

propagates in an algebra $X$

if $t(\mathbf y)$ holds whenever $t(\mathbf x)$ holds and all elements of $\mathbf y$ are in the subalgebra of $X$

generated by $\mathbf x$ . We offer results on propagating equations in general and on propagation of associativity in particular. We present several solutions to a problem of Rajah, who asked for a variety of loops in which Moufang theorem holds but that is not a subvariety of Moufang loops.

This is joint work with Aleš Drápal.