Submission: 2008, Dec 8
For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that K_i(A,\mathbb Z/m) = K_i(R,\mathbb Z/m) for any m relatively prime to the rank and i \geq 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semi-local rings and K-theory of graded central simple algebras indexed by a totally ordered abelian group.
2000 Mathematics Subject Classification: 19D99, 16H05, 18F25
Keywords and Phrases: Azumaya algebras, K-Theory
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