ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS

We study algebraic properties of powers of squarefree principal

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  • C. Andrei, V. Ene and B. Lajmiri, Powers of t-spread principal Borel ideals, Arch. Math. (Basel), 112(6) (2019), 587-597.
  • A. Aramova, J. Herzog and T. Hibi, Squarefree lexsegment ideals, Math. Z., 228(2) (1998), 353-378.
  • A. Aslam, The stable set of associated prime ideals of a squarefree principal Borel ideal, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 57(105) (2014), 243- 252.
  • M. Brodmann, Asymptotic stability of Ass(M=InM), Proc. Amer. Math. Soc., 74(1) (1979), 16-18.
  • M. Brodmann, The asymptotic nature of the analytic spread, Math. Proc. Cambridge Philos. Soc., 86 (1979), 35-39.
  • W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993.
  • E. De Negri, Toric rings generated by special stable sets of monomials, Math. Nachr., 203(1) (1999), 31-45.
  • D. Eisenbud, Commutative Algebra: with a view toward algebraic geometry, Graduate Texts in Mathematics, 150, Springer-Verlag, New York, 1995.
  • V. Ene and J. Herzog, Grobner Bases in Commutative Algebra, Graduate Studies in Mathematics, 130, American Mathematical Society, Providence, RI, 2012.
  • V. Ene, J. Herzog and A. Asloob Qureshi, t-spread strongly stable ideals, arXiv:1805.02368 [math.AC].
  • C. A. Francisco, Minimal graded Betti numbers and stable ideals, Comm. Algebra, 31(10) (2003), 4971-4987.
  • C. A. Francisco, J. Mermin and J. Schweig, Borel generators, J. Algebra, 332(1) (2011), 522-542.
  • J. Herzog and T. Hibi, The depth of powers of an ideal, J. Algebra, 291(2) (2005), 534-550.
  • J. Herzog and T. Hibi, Monomial Ideals, Graduate Texts in Mathematics, 260, Springer-Verlag London, Ltd., London, 2011.
  • J. Herzog and T. Hibi, Bounding the socles of powers of squarefree monomial ideals, Commutative Algebra and Noncommutative Algebraic Geometry, Vol. II, Math. Sci. Res. Inst. Publ., 68, Cambridge Univ. Press, New York, (2015), 223-229.
  • J. Herzog, A. Rauf and M. Vladoiu, The stable set of associated prime ideals of a polymatroidal ideal, J. Algebraic Combin., 37(2) (2013), 289-312.
  • G. Kalai, Algebraic shifting, in: Computational Commutative Algebra and Combinatorics, (Osaka, 1999), Adv. Stud. Pure Math., 33, Math. Soc. Japan, Tokyo, (2002), 121-163.
  • I. Peeva and M. Stillman, The minimal free resolution of a Borel ideal, Expo. Math., 26(3) (2008), 237-247.