### The Steinberg group of a monoid ring, nilpotence, and algorithms, by Joseph Gubeladze

For a regular ring R and an affine monoid M the homotheties of M act
nilpotently on the Milnor unstable groups of R[M]. This strengthens
the K_2 part of the main result of [G5] in two ways: the coefficient
field of characteristic 0 is extended to any regular ring and the
stable K_2-group is substituted by the unstable ones. The proof is
based on a polyhedral/combinatorial techniques, computations in
Steinberg groups, and a substantially corrected version of an old
result on elementary matrices by Mushkudiani. A similar stronger
nilpotence result for K_1 and algorithmic consequences for
factorization of high Frobenius powers of invertible matrices are also
derived.

See http://arxiv.org/abs/math/0601400.

Joseph Gubeladze <soso@math.sfsu.edu>