Milnor K-theory

In mathematics, Milnor K-theory^[1] is an algebraic invariant (denoted ${\displaystyle K_{*}(F)}$ for a field ${\displaystyle F}$) defined by John Milnor (1970) as an attempt to study higher algebraic K-theory in the special case of fields. It was hoped this would help illuminate the structure for algebraic K-theory and give some insight about its relationships with other parts of mathematics, such as Galois cohomology and the Grothendieck–Witt ring of quadratic forms. Before Milnor K-theory was defined, there existed ad-hoc definitions for ${\displaystyle K_{1}}$ and ${\displaystyle K_{2}}$. Fortunately, it can be shown Milnor K-theory is a part of algebraic K-theory, which in general is the easiest part to compute.^[2]