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A Gröbner Basis Algorithm for Ideals over Zero-Dimensional Valuation Rings

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Abstract

Zero-dimensional valuation rings are one kind of non-Noetherian rings. This paper investigates properties of zero-dimensional valuation rings and prove that a finitely generated ideal over such a ring has a Gröbner basis. The authors present an algorithm for computing a Gröbner basis of a finitely generated ideal over it. Furthermore, an interesting example is also provided to explain the algorithm.

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Authors and Affiliations

  1. College of Mathematics and Computations, Hunan University of Science and Technology, Xiangtan, 411201, China

    Dongmei Li & Jinwang Liu

Authors
  1. Dongmei Li
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  2. Jinwang Liu
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Corresponding author

Correspondence to Dongmei Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11871207 and 11971161.

This paper was recommended for publication by Editor FENG Ruyong.

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Li, D., Liu, J. A Gröbner Basis Algorithm for Ideals over Zero-Dimensional Valuation Rings. J Syst Sci Complex 34, 2470–2483 (2021). https://doi.org/10.1007/s11424-020-0010-3

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  • DOI: https://doi.org/10.1007/s11424-020-0010-3

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