K-theory spectrum

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

(K_{R})_{n}=K_{0}(\Sigma ^{n}R)\times BGL(\Sigma ^{n}R)^{+}

,

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

References

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

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