The Hermite ring conjecture and special linear groups for valuation rings

Jinwang Liu; Dongmei Li

paper

The Hermite ring conjecture and special linear groups for valuation rings

arXiv:1811.01230

Abstract

In this paper we prove that the Hermite ring conjecture holds for valuation rings $V$ , and the special liner group $S L_{n} (V [x])$ coincides with the group generated by elementary matrices $E_{n} (V [x])$ for $n \geq 3$ . For any arithmetical ring $R$ and $n \geq 3$ , we show $S L_{n} (R [x]) = S L_{n} (R) \cdot E_{n} (R [x])$ .

10 pages