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Monomial ideals with tiny squares and Freiman ideals

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Abstract

We provide a construction of monomial ideals in R = K[x, y] such that μ(I2) < μ(I), where μ denotes the least number of generators. This construction generalizes the main result of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018). Working in the ring R, we generalize the definition of a Freiman ideal which was introduced in J. Herzog, G. Zhu (2019) and then we give a complete characterization of such ideals. A particular case of this characterization leads to some further investigations on μ(Ik) that generalize some results of S. Eliahou, J. Herzog, M. Mohammadi Saem (2018), J. Herzog, M. Mohammadi Saem, N. Zamani (2019), and J. Herzog, A. Asloob Qureshi, M. Mohammadi Saem (2019).

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Authors and Affiliations

  1. Department of Mathematics, Sultan Qaboos University, P.O.Box 31, Muscat, Oman

    Ibrahim Al-Ayyoub

  2. Department of Mathematics and Statistics, Jordan University of Science and Technology, P.O.Box 3030, Irbid, 22110, Jordan

    Ibrahim Al-Ayyoub

  3. Department of Mathematics, Khayyam University, Mashhad, Iran

    Mehrdad Nasernejad

Authors
  1. Ibrahim Al-Ayyoub
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  2. Mehrdad Nasernejad
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Correspondence to Ibrahim Al-Ayyoub.

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Al-Ayyoub, I., Nasernejad, M. Monomial ideals with tiny squares and Freiman ideals. Czech Math J 71, 847–864 (2021). https://doi.org/10.21136/CMJ.2021.0124-20

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  • DOI: https://doi.org/10.21136/CMJ.2021.0124-20

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