Let ( R ,m) be a Noetherian local ring and M a finitely generated R-module. We say M has maximal depth if there is an associated prime p of M such that depth M = dim R/p . In this paper we study squarefree monomial ideals which have maximal depth. Edge ideals of cycle graphs, transversal polymatroidal ideals and high powers of connected bipartite graphs with this property are classified.

中文翻译：

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具有最大深度的无平方单项式理想

设 ( R ,m) 是诺特局部环，M 是有限生成的 R 模。如果存在 M 的相关质数 p 使得深度 M = dim R/p ，我们就说 M 具有最大深度。在本文中，我们研究具有最大深度的无平方单项式理想。对循环图的边理想、横向多拟阵理想和具有此性质的连通二部图的高次幂进行分类。