Invertibility of Matrices Over Subrings |
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Authors: | Mark Grinshpon |
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Institution: | 1. Department of Mathematics , Virginia Tech , Blacksburg, Virginia, USA grinshpon@vt.edu |
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Abstract: | Given rings R ? S, consider the division closure 𝒟(R, S) and the rational closure ?(R, S) of R in S. If S is commutative, then 𝒟(R, S) = ?(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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Keywords: | Determinants Division closure Invertible matrices Rational closure |
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