Suspension of a ring

In algebra, more specifically in algebraic K-theory, the suspension $$\Sigma R$$ of a ring R is given by $$\Sigma(R) = C(R)/M(R)$$ 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: $$K_i(R) \simeq K_{i+1}(\Sigma R)$$.