Suspension of a ring

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In algebra, more specifically in algebraic K-theory, the suspension $\backslash Sigma\; R$ of a ring R is given byWeibel, III, Ex. 1.15 $\backslash Sigma(R)\; =\; C(R)/M(R)$ 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: $K\_i(R)\; \backslash simeq\; K\_\{i+1\}(\backslash Sigma\; R)$.