In algebra, more specifically in

algebraic K-theory Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense o ...

, the suspension

\Sigma R

of a ring ''R'' is given byWeibel, III, Ex. 1.15

\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 Suspension or suspended may refer to: Science and engineering * Suspension (topology), in mathematics * Suspension (dynamical systems), in mathematics * Suspension of a ring, in mathematics * Suspension (chemistry), small solid particles suspend ...

in topology. One then has:

K_i(R) \simeq K_(\Sigma R)

References

* C. Weibel
The K-book: An introduction to algebraic K-theory
Algebra {{algebra-stub