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On Reduction Numbers of Products of Ideals

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Abstract

Let R be a standard graded algebra over an infinite field \(\mathbb {K}\) and M a finitely generated \({\mathbb Z}\)-graded R-module. Let \(I_1,\ldots I_m\) be graded ideals of R. The functions \(r(M/I_1^{a_1}\ldots I_m^{a_m}M)\) and \(r(I_1^{a_1}\ldots I_m^{a_m}M)\) are investigated and their asymptotical behaviours are given. Here, \(r(\bullet )\) stands for the reduction number of a finitely generated graded R-module \(\bullet \).

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Acknowledgements

We would like to express our thanks to the referee for his/her careful reading and good advice. This project is supported by NSFC (No. 11971338) and NSF of Shanghai (No. 19ZR14241000).

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, People’s Republic of China

    Dancheng Lu

  2. School of Mathematical Sciences, Shanghai Jiaotong University, Shanghai, 210030, People’s Republic of China

    Tongsuo Wu

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  1. Dancheng Lu
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  2. Tongsuo Wu
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Correspondence to Dancheng Lu.

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Communicated by Mohammad Taghi Dibaei.

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Lu, D., Wu, T. On Reduction Numbers of Products of Ideals. Bull. Iran. Math. Soc. 46, 1027–1033 (2020). https://doi.org/10.1007/s41980-019-00308-1

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  • DOI: https://doi.org/10.1007/s41980-019-00308-1

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