Algebraic K-theory#Matsumoto.27s theorem

The set of Matsumoto is a lemma from the mathematical subfield of K-theory, it is an explicit description for the second algebraic K-theory of a body on. The theorem is named after the Japanese mathematician Matsumoto Hideya.

Set of Matsumoto

There is a body and its second algebraic K theory, then:

In other words, is isomorphic to the cokernel of the Dehn invariant

Milnor K-theory (history)

Motivated by the set of Matsumoto defined Milnor later named after him, Milnor K-theory of bodies by

Ie as the quotient of the tensor algebra graduated components on the abelian group F × by the two-sided ideal, which of the elements of the form

Is generated for a ≠ 0.1. There is a mapping

That is for and by the theorem of Matsumoto also an isomorphism.

For, however, is not a isomorphism of the cokernel

Is the so-called K- indekomposable theory, in the case of equal number of bodies.

For modulo 2- torsion group isomorphic to Bloch.