In this paper, we prove an extension of a theorem of Marcus, which says that every subshift of finite type of entropy log n, n an integer, factors onto the full n-shift. Let p(x) be a monic polynomial, irreducible over ℚ, whose coefficients (except for the leading coefficient) are non-positive integers. Suppose C(λ) is the companion matrix of p(x), where λ is the largest real root of p(x) (λ exists, by the Perron-Frobenius theorem). Then for any aperiodic, non-negative, integral matrix A, with Perron value λ, we give necessary and sufficient conditions for the existence of a positive integer n and a right-closing map f: ΣA→ΣC(λ) satisfying fσn = σnf (where σ is the shift map).