Grothendieck Group

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

Famous quotes containing the word group:

    Remember that the peer group is important to young adolescents, and there’s nothing wrong with that. Parents are often just as important, however. Don’t give up on the idea that you can make a difference.
    —The Lions Clubs International and the Quest Nation. The Surprising Years, I, ch.5 (1985)