On the K-theory of truncated polynomial rings in non-commuting variables

TL;DR

This paper calculates the algebraic K-theory of a specific non-commutative ring formed by truncating polynomial rings over a perfect field of positive characteristic, using advanced Witt vector techniques.

Contribution

It provides the first explicit computation of the K-theory for these non-commutative truncated polynomial rings, connecting it with truncation poset Witt vectors.

Findings

Explicit formula for K-theory of the ring k<x_1,...,x_n>/(m^a)

Connection established between K-theory and truncation poset Witt vectors

Extension of K-theory computations to non-commutative polynomial rings

Abstract

We compute the algebraic K-theory of the non-commutative ring k<x_1,...,x_n>/(m^a) when k is a perfect field of positive characteristic and m=(x_1,...,x_n). We express the answer in terms of the truncation poset Witt vectors developed in [1].