Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2019, Cilt: 26 Sayı: 26, 224 - 244, 11.07.2019
https://doi.org/10.24330/ieja.587081

Öz

We study algebraic properties of powers of squarefree principal
Borel ideals I, and show that astab(I) = dstab(I). Furthermore, the behaviour
of the depth function depth S/I^k is considered.

Kaynakça

  • 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.
Yıl 2019, Cilt: 26 Sayı: 26, 224 - 244, 11.07.2019
https://doi.org/10.24330/ieja.587081

Öz

Kaynakça

  • 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.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Jurgen Herzog Bu kişi benim

Bahareh Lajmiri Bu kişi benim

Farhad Rahmati Bu kişi benim

Yayımlanma Tarihi 11 Temmuz 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 26 Sayı: 26

Kaynak Göster

APA Herzog, J., Lajmiri, B., & Rahmati, F. (2019). ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS. International Electronic Journal of Algebra, 26(26), 224-244. https://doi.org/10.24330/ieja.587081
AMA Herzog J, Lajmiri B, Rahmati F. ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS. IEJA. Temmuz 2019;26(26):224-244. doi:10.24330/ieja.587081
Chicago Herzog, Jurgen, Bahareh Lajmiri, ve Farhad Rahmati. “ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS”. International Electronic Journal of Algebra 26, sy. 26 (Temmuz 2019): 224-44. https://doi.org/10.24330/ieja.587081.
EndNote Herzog J, Lajmiri B, Rahmati F (01 Temmuz 2019) ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS. International Electronic Journal of Algebra 26 26 224–244.
IEEE J. Herzog, B. Lajmiri, ve F. Rahmati, “ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS”, IEJA, c. 26, sy. 26, ss. 224–244, 2019, doi: 10.24330/ieja.587081.
ISNAD Herzog, Jurgen vd. “ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS”. International Electronic Journal of Algebra 26/26 (Temmuz 2019), 224-244. https://doi.org/10.24330/ieja.587081.
JAMA Herzog J, Lajmiri B, Rahmati F. ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS. IEJA. 2019;26:224–244.
MLA Herzog, Jurgen vd. “ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS”. International Electronic Journal of Algebra, c. 26, sy. 26, 2019, ss. 224-4, doi:10.24330/ieja.587081.
Vancouver Herzog J, Lajmiri B, Rahmati F. ON THE ASSOCIATED PRIME IDEALS AND THE DEPTH OF POWERS OF SQUAREFREE PRINCIPAL BOREL IDEALS. IEJA. 2019;26(26):224-4.