Talk:Brauer group
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Brauer group of a variety
[edit]Anyone? Richard Pinch (talk) 06:12, 21 August 2008 (UTC)
Article needs to define what it means by "division algebra"
[edit]The following sentence:
"The finite-dimensional division algebras with center R (that means the dimension over R is finite) are the real numbers and the quaternions by a theorem of Frobenius, while any matrix ring over the reals or quaternions – M(n, R) or M(n, H) – is a CSA over the reals, but not a division algebra (if n > 1)"
shows that in this article, the octonions are not considered to be a division algebra over the reals. This implies that this article's definition of "division algebra" requires associativity.
But associativity of a division algebra is not automatically assumed in modern mathematics. Some authors assume associativity and others do not.
For this reason, it is important to state explicitly which definition of "division algebra" is being used in this article. ~2026-15500-14 (talk) 02:59, 16 April 2026 (UTC)