K-theory spectrum

In mathematics, given a ring R, the K-theory spectrum of R is an Ω-spectrum $K_{R}$ whose nth term is given by, writing $Σ R$ for the suspension of R,

(K_{R})_{n} = K_{0} (Σ^{n} R) \times B G L (Σ^{n} R)^{+}

,

where "+" means the Quillen's + construction.^[1] By definition, $K_{i} (R) = π_{i} (K_{R})$ .

References

↑ Dominique Arlettaz, Algebraic K-theory of rings from a topological view point [1]

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[1] Dominique Arlettaz, Algebraic K-theory of rings from a topological view point [1]

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