The Grothendieck group of a commutative monoid 
is the universal abelian group
receiving a homomorphism from 
. It is constructed from formal differences 
modulo the relation generated by 
. For vector bundles
under direct sum, the resulting group is the zeroth
K-group.
Grothendieck Group
See also
Abelian Group, Monoid, Universal Property, Vector BundleExplore with Wolfram|Alpha
References
Atiyah, M. F. K-Theory. Reading, MA: Addison-Wesley, 1989.Cite this as:
Weisstein, Eric W. "Grothendieck Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GrothendieckGroup.html