Talk:Azumaya algebra

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)

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

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)

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)

Todo

• Integrate references in https://web.archive.org/web/20200620001617/https://anagrams-seminar.github.io/brauer/azumayas.pdf to this article
• Integrate these notes as well: https://homepages.warwick.ac.uk/~maseap/arith/notes/quatrogiorno.pdf
• Add examples of Azumaya Algebra from https://arxiv.org/abs/1104.4333
• Also, Bourbaki Algebra Chapter 9 Section 9 Number 2 contains a relation between clifford algebras and azumaya algebras - https://mathoverflow.net/q/217798
• https://arxiv.org/abs/1307.7946

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