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Invertibility of Matrices over Subrings

Mark Grinshpon
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Abstract

Given 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.

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Mark Grinshpon. 2006-08-14. Invertibility of Matrices over Subrings. https://arxiv.org/abs/math/0603688

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