The Grothendieck-Witt ring GW is a related construction generated by isometry classes of nonsingular quadratic spaces with addition given by orthogonal sum and multiplication given by tensor product. Since two spaces that differ by a hyperbolic plane are not identified in GW, the inverse for the addition needs to be introduced formally through the construction that was discovered by Grothendieck (see Grothendieck group).
The hyperbolic spaces generate an ideal in GW and the Witt ring W is the quotient. The exterior power gives the Grothendieck-Witt ring the additional structure of a λ-ring.