Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1111-1124, 2020
Squarefree monomial ideals with maximal depth
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