Stanley’s conjecture for critical ideals-Reference-Cited by-同舟云学术

Stanley’s conjecture for critical ideals

Published:2011-06-01 Issue:2 Volume:48 Page:220-226
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
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Author:

Haider Azeem¹,Khan Sardar¹

Affiliation:

1. 1 GC University Abdus Salam School of Mathematical Sciences 68-B New Muslim Town, Lahore Pakistan

Abstract

Let S = K[x1,…,xn] be a polynomial ring in n variables over a field K. Stanley’s conjecture holds for the modules I and S/I, when I ⊂ S is a critical monomial ideal. We calculate the Stanley depth of S/I when I is a canonical critical monomial ideal. For non-critical monomial ideals we show the existence of a Stanley ideal with the same depth and Hilbert function.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://akademiai.com/doi/pdf/10.1556/sscmath.2010.1160

Reference8 articles.

1. Bruns, W. and Herzog, J., Cohen-Macaulay rings, Revised Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press (1993). MR95h:13020

2. Cimpoeas, M., Stanley depth of monomial ideals in three variables, arXiv: math. AC/0807.2166v3 (2008).

3. How to compute the Stanley depth of a monomial ideal;Herzog J.;J. Algebra,2009

4. The depth of an ideal with a given Hilbert function;Murai S.;Proc. Amedr. Math. Soc.,2008

5. Gotzmann ideals of the polynomial ring;Murai S.;Math. Z.,2008

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