The Hermite ring conjecture and special linear groups for valuation rings

2018/11/03 by Jinwang Liu, Dongmei Li, Liu, Jinwang +1
Mathematics · #13P05 #13P10 #15A06 #15A23 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13P05 #msc:13P10 #msc:15A06 #msc:15A23

paper · pdf · doi:10.48550/arxiv.1811.01230

10 pages

arxiv created 2018/11/03 · arxiv updated 2018/11/06

Abstract

In this paper we prove that the Hermite ring conjecture holds for valuation rings V, and the special liner group SL_n(V[x]) coincides with the group generated by elementary matrices E_n(V[x]) for n≥3. For any arithmetical ring R and n≥3, we show SL_n(R[x]) = SL_n(R)⋅ E_n(R[x]).

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