2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110357Given rings $R \subseteq S$, consider the division closure $DC(R,S)$ and the rational closure $RC(R,S)$ of R in S. If S is commutative, then $DC(R,S)=RC(R,S)=RT^{-1}$, where $T = \{t\in R : t^{-1} \in S\}$. We show that this is also true if we assume only that R is commutative.5 pages; minor revisions upon referee's suggestionsRings and Algebras16S50 (Primary) 13B30, 15A15 (Secondary)text