Every finite abelian group is the Brauer group of a ring
Every finite abelian group is the Brauer group of a ring
Given an arbitrary finite abelian group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a ring <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is constructed using cohomological techniques from algebraic geometry whose Brauer group is <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" …