In algebra, more specifically in algebraic K-theory, the suspension Σ R {\displaystyle \Sigma R} of a ring R is given by Σ ( R ) = C ( R ) / M ( R ) {\displaystyle \Sigma (R)=C(R)/M(R)} where C ( R ) {\displaystyle 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 ) {\displaystyle 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 ) {\displaystyle K_{i}(R)\simeq K_{i+1}(\Sigma R)} .
Notes
References C. Weibel "The K-book: An introduction to algebraic K-theory"