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Unimodular rows over monoid rings

Algebra & Discrete Mathematics

Speaker: Joseph Gubeladze
Location: 2112 MSB
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.