Invertibility of Matrices over Subrings

Details Invertibility of Matrices over Subrings Invertibility of Matrices over Subrings

2006-03-29

arxiv.org/abs/math/0603688v2

Mathematics

Rings and Algebras

5 pages; minor revisions upon referee's suggestions

Scientific paper

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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