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Math Help - Units in a matrix ring

  1. #1
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    Units in a matrix ring

    Let R be a commutative ring with 1. Characterize the units of M_n(R).

    If R is a field, then the usual characterization of the units are those matrices with non-zero determinant. But since R is just a commutative ring with 1 (and not even an integral domain) I have no idea how to characterization the units. Is there any nice way to do this?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Units in a matrix ring

    Quote Originally Posted by jgensler1992 View Post
    Let R be a commutative ring with 1. Characterize the units of M_n(R).
    A is a unit of \textrm{M}_n(R) if and only if |A| a is a unit of R .

    Hint : Use (\textrm{adj}\;B)B=B(\textrm{adj}\;B)=|B|I_n .
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