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Simplicial complexes with rigid depth

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Abstract

We extend a result of Minh and Trung (Adv. Math. 226:1285–1306, 2011) to get criteria for depth \({I = \rm {depth}\sqrt{I}}\) , where I is an unmixed monomial ideal of the polynomial ring S = K[x 1, . . . , x n ]. As an application we characterize all the pure simplicial complexes Δ which have rigid depth, that is, which satisfy the condition that for every unmixed monomial ideal \({I\subset S}\) with \({\sqrt{I}=I_\Delta}\) one has depth(I) = depth(I Δ).

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Authors and Affiliations

  1. Abdus Salam School of Mathematical Sciences (ASSMS), GC University, Lahore, Pakistan

    Adnan Aslam

  2. Faculty of Mathematics and Computer Science, Ovidius University, Bd. Mamaia 124, 900527, Constanta, Romania

    Viviana Ene

  3. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Viviana Ene

Authors
  1. Adnan Aslam
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  2. Viviana Ene
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Correspondence to Viviana Ene.

Additional information

Viviana Ene was supported by the grant UEFISCDI, PN-II-ID-PCE- 2011-3-1023.

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Aslam, A., Ene, V. Simplicial complexes with rigid depth. Arch. Math. 99, 315–325 (2012). https://doi.org/10.1007/s00013-012-0421-z

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  • DOI: https://doi.org/10.1007/s00013-012-0421-z

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