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Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration $M{<}_{deg}N$ such that ${}^{t}M{/}^{t+1}M{\simeq }^{t}N{/}^{t+1}N$ for all t. Given a module M with square-free top and a projective cover P, she showed that $di{m}_{k}Hom(M,M)=di{m}_{k}Hom(P,M)$ if and only if M has no proper degeneration $M{<}_{deg}N$ where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from our results....