Abstract

ABSTRACTWe prove that for any valuation ring R of Krull dimension ≤1 or any commutative local ring R with Krull dimension 0 and n≥3, the special linear group SLn(R[x]) coincides with the group of elementary matrices En(R[x]), and for an arbitrary arithmetical ring R of Krull dimension ≤1 and n≥3, the group . These give partial solutions to two conjectures of Yengui.

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