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Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations

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Abstract

In this paper, the notion of rational univariate representations with variables is introduced. Consequently, the ideals, created by given rational univariate representations with variables, are defined. One merit of these created ideals is that some of their algebraic properties can be easily decided. With the aid of the theory of valuations, some related results are established. Based on these results, a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.

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Correspondence to Shuijing Xiao or Guangxing Zeng.

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The authors declare no conflict of interest.

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This research was supported by the National Natural Science Foundation of China under Grant No. 12161057.

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Xiao, S., Zeng, G. Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations. J Syst Sci Complex 36, 2703–2724 (2023). https://doi.org/10.1007/s11424-023-2219-4

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  • DOI: https://doi.org/10.1007/s11424-023-2219-4

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