Action type geometrical equivalence of representations of groups

In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over $KF_{2}$where $F_{2}$ is a free group with $2$generators (compare with [Ca] where a continuum of non isomorphic simple $2$-generated groups is constructed). Using this fact we give an example of a non action type logically Noetherian representation (Section 9).