# Thread: Relative Brauer group is closed?

1. ## 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...

2. Originally Posted by percimbe
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?