  For a commutative Noetherian ring R of dimension d and a commutative
cancellative monoid M, the elementary action on unimodular n-rows over the
monoid ring R[M] is transitive for n>=max(d+2,3). The starting point is the
case of polynomial rings, considered by A. Suslin in the 1970s. The main result
completes a project, initiated in the early 1990s, and suggests a new direction
in the study of K-theory of monoid rings.
