序贯科恩-麦考利矩阵理想的表征

Pub Date : 2023-06-01 DOI:10.1142/s1005386723000196

Payman Mahmood Hamaali, A. Mafi, H. Saremi

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引用次数: 1

摘要

设[公式:见文]为[公式:见文]域中变量[公式:见文]中的多项式环，[公式:见文]为[公式:见文]的矩阵理想。我们证明，当且仅当[公式:见文本]具有线性商时，[公式:见文本]是顺序Cohen-Macaulay。因此，当且仅当[Formula: see text]是可shell时，[Formula: see text]是顺序Cohen-Macaulay。

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A Characterization of Sequentially Cohen–Macaulay Matroidal Ideals

Let [Formula: see text] be the polynomial ring in [Formula: see text] variables over a field [Formula: see text] and [Formula: see text] be a matroidal ideal of [Formula: see text]. We show that [Formula: see text] is sequentially Cohen–Macaulay if and only if the [Formula: see text] has linear quotients. As a consequence, [Formula: see text] is sequentially Cohen–Macaulay if and only if [Formula: see text] is shellable.

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