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Math Help - Relative Brauer group is closed?

  1. #1
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    Relative Brauer group is closed? Matrix ring/tensor product question.

    Hi there, any reference I have defines the RB group as a subgroup of a Brauer group, so I just wanted to check that my reasoning highlighted below is sound. My tensor product knowledge is a little rusty...

    Last edited by percimbe; May 6th 2010 at 04:36 AM.
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  2. #2
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    Quote Originally Posted by percimbe View Post
    Hi there, any reference I have defines the RB group as a subgroup of a Brauer group, so I just wanted to check that my reasoning highlighted below is sound. My tensor product knowledge is a little rusty...

    that highlighted part is correct. you should remember this useful identity that for any two K-algebras A,B we have M_m(A) \otimes_K M_n(B) \cong M_{mn}(A \otimes_K B).

    the problem in your proof is somewhere else, where you claimed that A^{op} \otimes_K L \cong A \otimes_K L. how would you prove this?
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