In mathematics, the Grothendieck group construction in abstract algebra constructs an abelian group from a commutative monoid in the most universal way. It takes its name from the more general construction in category theory, introduced by Alexander Grothendieck in his fundamental work of the mid-1950s that resulted in the development of K-theory, which led to his proof of the Grothendieck-Riemann-Roch theorem. The Grothendieck group is denoted by K or R.
Read more about Grothendieck Group: Universal Property, Explicit Construction, Grothendieck Group and Extensions, Grothendieck Groups of Exact Categories, Grothendieck Groups of Triangulated Categories, Examples
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