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Talk:Azumaya algebra

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I am sorry I do not understand the definition: "... makes the tensor product isomorphic to the r×r matrix algebra over R." The tensor product of which objects? Secondly, a definition of Azumaya algebras over arbitrary commutative rings seems to be standard. Does anyone know a reference? Finally, what is the "reduced trace" in this context? Ninte 13:09, 6 January 2007 (UTC)[reply]

Okay, I found a textbook myself where everything is explained (Knus/Ojanguren, Springer Lecture Notes 389) Ninte 10:18, 12 January 2007 (UTC)[reply]

I did not know that this page existed. I suggest that the Azumaya algebra_s_ page is merged into this one as soon as possible.YogaYak (talk) 12:18, 17 October 2008 (UTC)[reply]

The section on the Skolem-Noether is dubious. It stated that the automorphisms were inner over an base ring, which is false in general: finite torsion in the Picard group can create obstructions. I added the word "local" as a quick-and-dirty fix, but the rest of the section should be examined. — Preceding unsigned comment added by 2A02:1810:3E15:4200:F18F:55AD:3839:82CF (talk) 15:16, 14 March 2021 (UTC)[reply]

Todo

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Wundzer (talk) 16:26, 22 June 2020 (UTC)[reply]