On the space of Sylvester matrix rank functions

Given a ring $R$, the notion of Sylvester rank function was conceived within the context of Cohn's classification theory of epic division $R$-rings. In this paper we study and describe the space of Sylvester rank functions on certain families of rings, including Dedekind domains, simple left noetherian rings and skew Laurent polynomial rings $\mathcal{D}[t^{\pm 1};τ]$ for any division ring $\mathcal{D}$ and any automorphism $τ$ of $\mathcal{D}$.

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