Abstract

Let $\cal V$ be a variety of algebras with a finite list of finite directly indecomposable members. We show that there is a polynomial time algorithm that tests the isomorphism between any two finite algebras from $\cal V.$ This includes the following classical structures in algebra:Abelian groups with $nx=0$, $n>0$,Boolean algebras,Rings with $x^m=x$, $m>1$,Modules over a finite semisimple ring.