Suspension of a ring

In algebra, more specifically in algebraic K-theory, the suspension formula_1 of a ring "R" is given by formula_2 where formula_3 is the ring of all infinite matrices with coefficients in "R" having only finitely many nonzero elements in each row or column and formula_4 is its ideal of matrices having only finitely many nonzero elements. It is an analog of suspension in topology.
One then has: formula_5.