Hilbert coefficients of ideals under perturbation of an ideal
Tập 133 Số 1B (2024), Nghiên cứu
Tập 133 Số 1B (2024)

Hilbert coefficients of ideals under perturbation of an ideal

Nghiên cứu
https://doi.org/10.26459/hueunijns.v133i1B.7062
Đã xuất bản 2024-06-27
Cao Huy Linh
Department of Mathematics, College of Education, Hue University , 34 Le Loi, Hue, Vietnam
Ton That Quoc Tan
Department of Mathematics, FPT University, Danang , Viet Nam

Tóm tắt

Let (R, m) be a noetherian local ring, J an m-primary ideal of R and
I = (f1, ..., fr) an ideal generated by a filter regular sequence f1, ..., fr of R. In this
paper, we will prove the preserve of Hilbert coefficients of R/I with respect to J
under J-adic perturbation of I, provided that J is a parameter ideal generated by a
d-sequence of R/(f1, ..., fi) for i = 1, ..., r.

 

https://doi.org/10.26459/hueunijns.v133i1B.7062
PDF (English)

Tài liệu tham khảo

  1. Srinivas V,Trivedi V. The invariance of Hilbert functions of quotients under small perturbations. J Algebra. 1996;186(1):1-19.
  2. Ma L, Quy PH, I. Smirnov. Filter regular sequence under small perturbations. Math Ann. 2020;378(1-2):243-254.
  3. Quy PH, Trung NV. When does a perturbation of the equations preserve the normal cone. Trans Amer Math Soc. 2023;376:4957-4978.
  4. Linh CH. Upper bound for Castelnuovo-Mumford regularity of associated graded modules, Comm in Algebra. 2005;33(6):1817-1831.
  5. Vasconcelos W. The homological degree of module. Trans Amer Math Soc. 1998;350:1167-1179.
  6. Trung NV. The Castelnuovo regularity of the Rees Algebra and the associated graded ring. Trans Amer Math Soc. 1998;350(7):2813-2832.
  7. Trung NV. Absolutely superficial sequences. Math Proc Camb Phil Soc. 1983;93:35-47.
Creative Commons License

công trình này được cấp phép theo Creative Commons Ghi công-Chia sẻ tương tự 4.0 License International .

Bản quyền (c) 2024 Array