We show that for any finite-dimensional algebra Λ of infinite representation type, over a perfect field, there is a bounded principal ideal domain Γ and a representation embedding from Γ -mod into Λ -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.
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Ramos et al. (2024) studied this question.
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