Let R be a Dubrovin valuation ring of a simple Artinian ring Q and let Q[X,σ] be the skew polynomial ring over Q in an indeterminate X, where σ is an automorphism of Q. Consider the natural map φ from Q[X,σ]XQ[X,σ] to Q, where Q[X,σ]XQ[X,σ] is the localization of Q[X,σ] at the maximal ideal XQ[X,σ] and set \(\widetilde{R}=\varphi^{-1}(R)\) , the complete inverse image of R by φ. It is shown that \(\widetilde{R}\) is a Dubrovin valuation ring of Q(X,σ) (the quotient ring of Q[X,σ]) and it is characterized in terms of X and Q. In the case where R is an invariant valuation ring, the given automorphism σ is classified into five types, in order to study the structure of \(\Gamma_{\widetilde{R}}\) (the value group of \(\widetilde{R}\) ). It is shown that there is a commutative valuation ring R with automorphism σ which belongs to each type and which makes \(\Gamma_{\widetilde{R}}\) Abelian or non-Abelian. Furthermore, some examples are used to show that several ideal-theoretic properties of a Dubrovin valuation ring of Q with finite dimension over its center, do not necessarily hold in the case where Q is infinite-dimensional.