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Squarefree monomial ideals with maximal depth. (English) Zbl 07285983

Summary: 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.

MSC:

13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
05E40 Combinatorial aspects of commutative algebra
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