Hermite Ring Conjecture on Valuation Rings

Jin Wang LIU, Dong Mei LI, Tao WU

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 387-392.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 387-392. DOI: 10.12386/A2022sxxb0030

Hermite Ring Conjecture on Valuation Rings

  • Jin Wang LIU, Dong Mei LI, Tao WU
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Abstract

This paper mainly studies the Hermite ring conjecture on valuation rings. According to the properties of the univariate polynomial ring V[x] on the valuation ring V, we investigate and obtain a series of equivalent properties for the unimodular row vector (a1(x),a2(x),…,an(x)) on V[x]. And then we prove that the Hermite ring conjecture on the valuation ring holds, that is, for an arbitrary valuation ring V, V[x] is a Hermite ring.

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valuation ring / Serre conjecture / Hermite ring conjecture

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Jin Wang LIU, Dong Mei LI, Tao WU. Hermite Ring Conjecture on Valuation Rings. Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 387-392 https://doi.org/10.12386/A2022sxxb0030

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