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Keywords:
Freiman ideal; number of generator; power of ideal; Ratliff-Rush closure
Freiman ideal; number of generator; power of ideal; Ratliff-Rush closure
Summary:
We provide a construction of monomial ideals in $R=K[x,y]$ such that $\mu (I^{2})< \nobreak \mu (I)$, where $\mu $ 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 $\mu (I^{k})$ 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).
References:
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