Czechoslovak Mathematical Journal, first online, pp. 1-14


Squarefree monomial ideals with maximal depth

Ahad Rahimi

Received April 10, 2019.   Published online April 20, 2020.

Abstract:  Let $(R,\mathfrak m)$ be a Noetherian local ring and $M$ a finitely generated $R$-module. We say $M$ has maximal depth if there is an associated prime $\mathfrak p$ of $M$ such that depth $M=\dim R/\mathfrak p$. 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.
Keywords:  maximal depth; cycle graph; line graph; whisker graph; transversal polymatroidal ideal; power of edge ideal
Classification MSC:  13C15, 05E40
DOI:  10.21136/CMJ.2020.0171-19

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Affiliations:   Ahad Rahimi, Department of Mathematics, Razi University, Taghe-Bostan, University St., Kermanshah, Iran, e-mail: ahad.rahimi@razi.ac.ir


 
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