Minimal free resolutions and the arithmetical rank of Stanley-Reisner ideals

斯坦利-赖斯纳理想的最小自由分辨率和算术等级

• 批准号: 23540053
• 负责人: TERAI Naoki
• 金额: $ 3.24万
• 依托单位: Saga University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540053/
• 关键词: Stanley-Reisner ideal; minimal free resolution; arithmetical rank; Stanley-Reisner イデアル; 算術階数; 極小自由分解; Ｓｔａｎｌｅｙ－Ｒｅｉｓｎｅｒ イデアル

We studied the arithmetical rank of Stanly-Reisner ideals, which are squarefree monomial ideals in a polynomial ring. It is known that the arithmetical rank of a Stanley-Reisner ideal is greater than or equal to the projective dimension of the Stanley-Reisner ring, which is the length of the minimal free resolutions of the quotient ring. As for the edge ideal of a forest, Barile conjectures that these numbers will be coincident. We proved it. As for a Gorenstein Stanly-Reisner ideal of height three, we proved that its arithmetical rank is equal to the projective dimension of the Stanly-Reisner ring, too.

本文研究了多项式环中无平方根单项理想Stanly-Reisner理想的算术秩。已知Stanley-Reisner理想的算术秩大于或等于Stanley-Reisner环的投射维数，即商环的最小自由分解的长度。至于森林的边缘理想，Barile指出这些数字将是重合的。对于高度为3的Gorenstein Stanly-Reisner理想，我们也证明了它的算术秩等于Stanly-Reisner环的投射维数。

项目成果

Binomial arithmetical rank of edge ideals of forests

• DOI: 10.1090/s0002-9939-2013-11473-5
• 发表时间: 2013-01
• 作者: K. Kimura;N. Terai

Pure and Cohen–Macaulay Simplicial Complexes Associated with Squarefree Lexsegment Ideals

• DOI: 10.1080/00927872.2011.605409
• 发表时间: 2012-09
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: V. Bonanzinga;L. Sorrenti;N. Terai

ヤング図形とsquarefree monomial idealの記号的冪の射影次元

杨形和无平方单项式理想的象征力的射影维数

• 发表时间: 2012
• 作者: 張間忠人;渡辺純三;南沙也加;南沙也加;藤澤太郎;Yoshio Fujimoto;藤澤太郎;M. Barile and N. Terai;藤本圭男;藤本圭男;Naoki Terai;寺井直樹
• 通讯作者: 寺井直樹

Cohen-Macaulayness of large powers of Stanley-Reisner ideals

• DOI: 10.1016/j.aim.2011.10.004
• 发表时间: 2010-09
• 期刊: arXiv: Commutative Algebra
• 作者: N. Terai;N. Trung

Licci sqarefree monomial ideals generated in degree two or with deviation two

Licci 以二级或偏差二级生成的无方单项式理想

• 发表时间: 2013
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Kyoko Kimura;Naoki Terai,Ken-ichi;Yoshida
• 通讯作者: Yoshida