What is Suspension of a ring?

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

One then has: K i ≃ K i + 1 {\displaystyle K_{i}\simeq K_{i+1}}.