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 Grothendieck-Witt ring GW is a related construction generated by isometry classes of nonsingular quadratic spaces, utilizing addition as orthogonal sum and multiplication as tensor product. Because two spaces differing by a hyperbolic plane are not distinguished in GW, the inverse for the addition must be formally introduced through the construction discovered by Grothendieck (see Grothendieck group).