A representation embedding for algebras of infinite type

We show that for any finite-dimensional algebra of infinite representation type, over a perfect field, there is a bounded principal ideal domain and a representation embedding from -mod into -mod. As an application, we prove a variation of the Brauer-Trall Conjecture II: finite-dimensional algebras of infinite-representation type admit infinite families of non-isomorphic finite-dimensional indecomposables with fixed endolength, for infinitely many endolengths.