Suspension of a ring

In algebra, more specifically in algebraic K-theory, the suspension $\mathrm{\Sigma }R$ of a ring R is given by $\mathrm{\Sigma }(R)=C(R)/M(R)$ where $C(R)$ is the ring of all infinite matrices with entries in R having only finitely many nonzero elements in each row or column and $M(R)$ is its ideal of matrices having only finitely many nonzero elements. It is an analog of suspension in topology.

One then has: $K_i(R)\simeq K_{i+1}(\mathrm{\Sigma }R)$.

References

• C. Weibel "The K-book: An introduction to algebraic K-theory"