Nice group structure on the elementary orbit space of unimodular rows. (English) Zbl 1474.13018
Summary:
- (1)
- Let \(R\) be an affine algebra of dimension \(d\geq 5\) over \(\overline{\mathbb{F}}_p\) with \(p>3\). Then the group structure on \(\operatorname{Um}_d(R)/\operatorname{E}_d(R)\) is nice.
- (2)
- Let \(R\) be a commutative noetherian ring of dimension \(d\geq 2\) such that \(\text{E}_{d+1}(R)\) acts transitively on \(\operatorname{Um}_{d+1}(R)\). Then the group structure on \(\operatorname{Um}_{d+1}(R[X])/\text{E}_{d+1}(R [X])\) is nice.
MSC:
| 13C10 | Projective and free modules and ideals in commutative rings |
| 19D45 | Higher symbols, Milnor \(K\)-theory |
| 19G12 | Witt groups of rings |
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