On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals

1998 ◽  
Vol 229 (3) ◽  
pp. 519-537 ◽  
Author(s):  
Lê Tuân Hoa ◽  
Ngô Viêt Trung
Keyword(s):  
Monomial Ideals ◽  
Arithmetic Degree

scholarly journals Arithmetical rank of squarefree monomial ideals of small arithmetic degree

2008 ◽  
Vol 29 (3) ◽  
pp. 389-404 ◽  
Author(s):  
Kyouko Kimura ◽  
Naoki Terai ◽  
Ken-ichi Yoshida
Keyword(s):  
Monomial Ideals ◽  
Arithmetical Rank ◽  
Arithmetic Degree

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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