Suspension of a ring

In algebra, more specifically in algebraic K-theory, the suspension \Sigma R of a ring R is given by[1] \Sigma(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) \simeq K_{i+1}(\Sigma R).

References

  1. ↑ Weibel, III, Ex. 1.15


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