Unimodular rows over monoid ringsAlgebra & Discrete Mathematics
|Start time:||Wed, Jan 17 2018, 4:10PM|
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+1,2). The starting point is the case of polynomial rings, considered by A. Suslin in the 1970s. The method of proof is a combination of the commutative algebra, surrounding Suslin's argument, and a polytopal pyramidal induction. 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.