Monomial Ideals with Tiny Squares and Freiman Ideals

被引：2

作者：

Al-Ayyoub, Ibrahim ^{[1
,2
]}

Nasernejad, Mehrdad ^{[3
]}

机构：

[1] Sultan Qaboos Univ, Dept Math, POB 31, Muscat, Oman

[2] Jordan Univ Sci & Technol, Dept Math & Stat, POB 3030, Irbid 22110, Jordan

[3] Khayyam Univ, Dept Math, Mashhad, Razavi Khorasan, Iran

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2021年 / 71卷 / 03期

关键词：

Freiman ideal; number of generator; power of ideal; Ratliff-Rush closure;

D O I：

10.21136/CMJ.2021.0124-20

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a construction of monomial ideals in R = K[x, y] such that mu(I-2) < 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).

引用

页码：847 / 864

页数：18

共 11 条

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Zhu, Guangjun
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