关于一些图运算下无平方单理想和覆盖理想的正规性的结果

Pub Date : 2021-11-30 DOI:10.7146/math.scand.a-128963

Ibrahim Al-Ayyoub, M. Nasernejad, K. Khashyarmanesh, L. Roberts, V. C. Quiñonez

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引用次数: 2

摘要

在这篇文章中，我们介绍了从旧的无平方的正规单项式理想产生的技术。然后，这些技术被用来研究覆盖理想在一些图运算下的正规性。作为两个正规理想的线性组合出现的无平方的单项式理想被证明不一定是正规的；在这种情况下，我们研究了这些理想的所有幂的整体封闭性。

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Results on the normality of square-free monomial ideals and cover ideals under some graph operations

In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover ideals under some graph operations. Square-free monomial ideals that come out as linear combinations of two normal ideals are shown to be not necessarily normal; under such a case we investigate the integral closedness of all powers of these ideals.

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