Unimodular rows over monoid rings

2017/06/14 by Gubeladze, Joseph · 3 citations
#19B14 (Primary) #20M25 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1706.04364

Abstract

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.

Cited by

• Subintegrality and ideal class groups of monoid algebras
• A generalization of Rao's theorem to graded R-subalgebras of R[t]
• On Projective modules over graded R-subalgebras of R[X,1/X]

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