Invertibility of Matrices over Subrings
Mark Grinshpon
Abstract
Given rings R ⊂eq 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∈ R : t-1 ∈ S\. We show that this is also true if we assume only that R is commutative.
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