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$ K$-theory of Azumaya algebras


Author: Charles A. Weibel
Journal: Proc. Amer. Math. Soc. 81 (1981), 1-7
MSC: Primary 18F25
DOI: https://doi.org/10.1090/S0002-9939-1981-0589125-6
MathSciNet review: 589125
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Abstract: Quillen has defined a $ K$-theory for symmetric monoidal categories. We show that Quillen's groups agree with the groups $ {K_0}$, $ {K_1}$, and $ {K_2}$ defined by Bass. Finally, we compute the $ K$-theory of the Azumaya algebras over a commutative ring.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0589125-6
Keywords: Algebraic $ K$-theory, Azumaya algebra, infinite loop space, symmetric monoidal category
Article copyright: © Copyright 1981 American Mathematical Society

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