Coarsification of hte module isomorphism relation Peteris Daugulis Department of Mathematics, Daugavpils University Parades 1, Daugavpils, Latvia September 1, 2006 Abstract In this paper new equivalence relations on the category Mod(A) for any associative algebra A and several related results are given. The new equivalence relations are defined using restrictions to subalgebras and the action of algebra automorphisms on modules. MSV 16G30, 16G60.