与路径和循环相关的阿尔丁代数的弱勒夫谢茨性质

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2024-08-14 DOI:10.1007/s40306-024-00549-1

Hop D. Nguyen, Quang Hoa Tran

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引用次数: 0

摘要

给定特征为零的基域 \(\Bbbk \)，对于每个图 G，我们关联由 G 的边理想和变量平方定义的artinian代数 A(G)。我们研究了 A(G) 的弱莱夫谢茨性质。我们划分了几类边缘相对较少（包括路径和循环）的图，这些图的相关artinian环具有弱Lefschetz性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles

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The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles

Given a base field \(\Bbbk \) of characteristic zero, for each graph G, we associate the artinian algebra A(G) defined by the edge ideal of G and the squares of the variables. We study the weak Lefschetz property of A(G). We classify some classes of graphs with relatively few edges, including paths and cycles, such that its associated artinian ring has the weak Lefschetz property.

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来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.