Milnor-Witt K-Theory and Tensor Powers of the Augmentation Ideal of ℤ[F×]

Abstract

Let F be a field of characteristic not equal to 2. We describe the relation between the non-negative dimensional Milnor-Witt K-theory of F and the tensor algebra over the group ring ℤ[F×] of the augmentation ideal [Formula: see text]. In the process, we clarify the structure of the additive group [Formula: see text], giving a simple presentation in particular.