scholarly journals Stanley conjecture on monomial ideals of mixed products

2015 ◽  
Vol 7 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Gaetana Restuccia ◽  
Zhongming Tang ◽  
Rosanna Utano
Keyword(s):  
Monomial Ideals ◽  
Stanley Conjecture

scholarly journals Stanley depth of monomial ideals with small number of generators

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Mircea Cimpoeaş
Keyword(s):  
Monomial Ideal ◽  
Monomial Ideals ◽  
Stanley Depth ◽  
Number Of Generators ◽  
Stanley Conjecture

AbstractFor a monomial ideal I ⊂ S = K[x 1...,x n], we show that sdepth(S/I) ≥ n − g(I), where g(I) is the number of the minimal monomial generators of I. If I =νI′, where ν ∈ S is a monomial, then we see that sdepth(S/I) = sdepth(S/I′). We prove that if I is a monomial ideal I ⊂ S minimally generated by three monomials, then I and S/I satisfy the Stanley conjecture. Given a saturated monomial ideal I ⊂ K[x 1,x 2,x 3] we show that sdepth(I) = 2. As a consequence, sdepth(I) ≥ sdepth(K[x 1,x 2,x 3]//I) +1 for any monomial ideal in I ⊂ K[x 1,x 2,x 3].

On Stanley Depths of Certain Monomial Factor Algebras

2015 ◽  
Vol 58 (2) ◽  
pp. 393-401
Author(s):  
Zhongming Tang
Keyword(s):  
Polynomial Ring ◽  
Monomial Ideal ◽  
Primary Decomposition ◽  
Factor Algebra ◽  
Stanley Depth ◽  
Stanley Conjecture ◽  
Stanley Decomposition

AbstractLet S = K[x1 , . . . , xn] be the polynomial ring in n-variables over a ûeld K and I a monomial ideal of S. According to one standard primary decomposition of I, we get a Stanley decomposition of the monomial factor algebra S/I. Using this Stanley decomposition, one can estimate the Stanley depth of S/I. It is proved that sdepthS(S/I) ≤ sizeS(I). When I is squarefree and bigsizeS(I) ≤ 2, the Stanley conjecture holds for S/I, i.e., sdepthS(S/I) ≥ depthS(S/I).

scholarly journals A-graded methods for monomial ideals

2009 ◽  
Vol 322 (8) ◽  
pp. 2886-2904 ◽  
Author(s):  
Christine Berkesch ◽  
Laura Felicia Matusevich
Keyword(s):  
Monomial Ideals

Irreducible decomposition of monomial ideals

2005 ◽  
Vol 39 (3) ◽  
pp. 99-99 ◽  
Author(s):  
Shuhong Gao ◽  
Mingfu Zhu
Keyword(s):  
Monomial Ideals ◽  
Irreducible Decomposition

Unmixed Monomial Ideals of Dimension Two and Their Cohen–Macaulay Properties

2010 ◽  
Vol 38 (5) ◽  
pp. 1699-1714 ◽  
Author(s):  
Nguyen Cong Minh ◽  
Yukio Nakamura
Keyword(s):  
Monomial Ideals

scholarly journals Stanley’s conjecture for critical ideals

2011 ◽  
Vol 48 (2) ◽  
pp. 220-226
Author(s):  
Azeem Haider ◽  
Sardar Khan
Keyword(s):  
Polynomial Ring ◽  
Hilbert Function ◽  
Monomial Ideal ◽  
Monomial Ideals ◽  
Stanley Depth

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.

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