Suspension of a ring

In algebra, more specifically in algebraic K-theory, the suspension [math]\displaystyle{ \Sigma R }[/math] of a ring R is given by [math]\displaystyle{ \Sigma(R) = C(R)/M(R) }[/math] where [math]\displaystyle{ C(R) }[/math] is the ring of all infinite matrices with entries in R having only finitely many nonzero elements in each row or column and [math]\displaystyle{ M(R) }[/math] is its ideal of matrices having only finitely many nonzero elements. It is an analog of suspension in topology. One then has: [math]\displaystyle{ K_i(R) \simeq K_{i+1}(\Sigma R) }[/math].

References

• C. Weibel "The K-book: An introduction to algebraic K-theory"