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Title: Squarefree monomial ideals with maximal depth (English)
Author: Rahimi, Ahad
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 70
Issue: 4
Year: 2020
Pages: 1111-1124
Summary lang: English
Category: math
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. (English)
Keyword: maximal depth
Keyword: cycle graph
Keyword: line graph
Keyword: whisker graph
Keyword: transversal polymatroidal ideal
Keyword: power of edge ideal
MSC: 05E40
MSC: 13C15
idZBL: 07285983
idMR: MR4181800
DOI: 10.21136/CMJ.2020.0171-19
Date available: 2020-11-18T09:48:07Z
Last updated: 2021-02-10
Stable URL:
Reference: [1] Brodmann, M.: Asymptotic stability of Ass$(M/I^n M)$.Proc. Am. Math. Soc. 74 (1979), 16-18. Zbl A0395.13008, MR 0521865, 10.2307/2042097
Reference: [2] Bruns, W., Herzog, J.: Cohen-Macaulay Rings.Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, Cambridge (1998). Zbl 0909.13005, MR 1251956, 10.1017/cbo9780511608681
Reference: [3] Faridi, S.: Simplicial trees are sequentially Cohen-Macaulay.J. Pure Appl. Algebra 190 (2004), 121-136. Zbl 1045.05029, MR 2043324, 10.1016/j.jpaa.2003.11.014
Reference: [4] Francisco, C. A., Hà, H. T.: Whiskers and sequentially Cohen-Macaulay graphs.J. Comb. Theory, Ser. A 115 (2008), 304-316. Zbl 1142.13021, MR 2382518, 10.1016/j.jcta.2007.06.004
Reference: [5] Frühbis-Krüger, A., Terai, N.: Bounds for the regularity of monomial ideals.Mathematiche, Suppl. 53 (1998), 83-97. Zbl 0951.13017, MR 1696019
Reference: [6] Herzog, J., Hibi, T.: Monomial Ideals.Graduate Texts in Mathematics 260, Springer, London (2011). Zbl 1206.13001, MR 2724673, 10.1007/978-0-85729-106-6
Reference: [7] Herzog, J., Rauf, A., Vladoiu, M.: The stable set of associated prime ideals of a polymatroidal ideal.J. Algebr. Comb. 37 (2013), 289-312. Zbl 1258.13014, MR 3011344, 10.1007/s10801-012-0367-z
Reference: [8] Jacques, S.: Betti Numbers of Graph Ideals: Ph.D. Thesis.University of Sheffield, Sheffield (2004), Available at\kern0pt.
Reference: [9] Lam, H. M., Trung, N. V.: Associated primes of powers of edge ideals and ear decompositions of graphs.Trans. Am. Math. Soc. 372 (2019), 3211-3236. Zbl 1420.13023, MR 3988608, 10.1090/tran/7662
Reference: [10] Martínez-Bernal, J., Morey, S., Villarreal, R. H.: Associated primes of powers of edge ideals.Collect. Math. 63 (2012), 361-374. Zbl 1360.13027, MR 2957976, 10.1007/s13348-011-0045-9
Reference: [11] Miller, E., Sturmfels, B., Yanagawa, K.: Generic and cogeneric monomial ideals.J. Symb. Comput. 29 (2000), 691-708. Zbl 0955.13008, MR 1769661, 10.1006/jsco.1999.0290
Reference: [12] Rahimi, A.: Maximal depth property of finitely generated modules.J. Algebra Appl. 17 (2018), Article ID 1850202, 12 pages. Zbl 1409.13023, MR 3879078, 10.1142/S021949881850202X
Reference: [13] Villarreal, R. H.: Monomial Algebras.Monographs and Research Notes in Mathematics, CRC Press, Boca Raton (2015). Zbl 1325.13004, MR 3362802, 10.1201/b18224

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