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In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum K R {\displaystyle K_{R}} whose nth term is given by, writing Σ R {\displaystyle \Sigma R} for the suspension of R,
where "+" means the Quillen's + construction. By definition, K i = π i {\displaystyle K_{i}=\pi _{i}}.
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