FUNCTORS PRESERVING TAMENESS

Let LAMBDA = k[Q]/I be a basic and connected finite-dimensional algebra over an algebraically closed field k. For each dimension vector z is-an-element-of N(Q0), we denote by mod LAMBDA-(z) the variety of LAMBDA-modules of dimension type z and by ind LAMBDA-(z) the constructible subset of indecomposable modules. We prove that LAMBDA is a tame algebra if and only if for each z is-an-element-of N(Q0), any constructible subset C of ind LAMBDA-(z) is at most one-dimensional provided different modules in C are not isomorphic. We apply this criterion to show that tameness is preserved by Ext functors and under suitable assumptions by Galois covering functors.