The Steinberg group of a monoid ring, nilpotence, and algorithms

Details The Steinberg group of a monoid ring, nilpotence, and algorithms The Steinberg group of a monoid ring, nilpotence, and algorithms

2006-01-17

arxiv.org/abs/math/0601400v3

Mathematics

K-Theory and Homology

final version, to appear in Journal of Algebra

Scientific paper

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 [Mu]. A similar stronger nilpotence result for K_1 and algorithmic consequences for factorization of high Frobenius powers of invertible matrices are also derived.

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