Abstract
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.
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Acknowledgments
I would like to thank Jürgen Herzog for helpful discussions on this work. I would also like to thank the referee for helpful comments on this article.
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Rahimi, A. Squarefree Monomial Ideals with Maximal Depth. Czech Math J 70, 1111–1124 (2020). https://doi.org/10.21136/CMJ.2020.0171-19
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DOI: https://doi.org/10.21136/CMJ.2020.0171-19