Suspension of a ring

In algebra, more specifically in algebraic K-theory, the suspension Σ R of a ring R is given by Σ ( R ) = C ( R ) / M ( R ) where C ( R ) is the ring of all infinite matrices with coefficients 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 ) ≃ K i + 1 ( Σ R ) .