Baer-Kaplansky classes of vector spaces and modules determined by numerical invariants

We show that reasonably large classes (Formula presented.) of vector spaces, modules over noncommutative algebras and abelian groups are Baer-Kaplansky classes with additional properties. Indeed, modules in (Formula presented.) such that their endomorphism rings are isomorphic vector spaces, or modules such that their endomorphism rings are isomorphic vector spaces with the same number of primitive idempotents may be actually isomorphic.