The elementary action on unimodular rows over a monoid ring. II
Let \(R\) be a commutative Noetherian ring with finite Krull dimension \(d\) and \(M\) an additive submonoid of \(\mathbb{Q}^ r_ +\) for some \(r \geq 1\). In part I [J. Algebra 148, 135-161 (1992; Zbl 0795.20056)], the author showed that when \(M \subset \mathbb{Q}^ r_ +\) is an integral extension, the group \(E_ n(R[M])\) of elementary matrices acts transitively on the set \(Um_ n (R[M])\) of unimodular rows of all \(n \geq \max(d+2,3)\). In this paper, the author extends this result to the class of submonoids of \(\mathbb{Q}^ r_ +\) of \(\Phi\)-simplicial growth, i.e., those monoids \(M\) which admit a sequence of finite convex polyhedra \(P_ 1 \subset P_ 2 \subset \dots \subset P_ k = \Phi(M)\) such that \(P_ 1\) and the closures (in the sense of Euclidean metric) of \(P_{i + 1} - P_ i\) are simplices for each \(1 \leq i \leq k - 1\).
scientific article; zbMATH DE number 168185