Stanley depth of squarefree monomial ideals
نویسندگان
چکیده
منابع مشابه
On the Stanley Depth of Squarefree Veronese Ideals
Let K be a field and S = K[x1, . . . ,xn]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth(M), and conjectured that depth(M) ≤ sdepth(M) for all finitely generated S-modules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zheng recently proposed a method of attack in the case when M = I/J with J ⊂ I being monomial S-ide...
متن کاملStanley Depth of the Integral Closure of Monomial Ideals
Let I be a monomial ideal in the polynomial ring S = K[x1, . . . , xn]. We study the Stanley depth of the integral closure I of I. We prove that for every integer k ≥ 1, the inequalities sdepth(S/Ik) ≤ sdepth(S/I) and sdepth(Ik) ≤ sdepth(I) hold. We also prove that for every monomial ideal I ⊂ S there exist integers k1, k2 ≥ 1, such that for every s ≥ 1, the inequalities sdepth(S/I1) ≤ sdepth(S...
متن کاملAn Algorithm to Compute the Stanley Depth of Monomial Ideals
Let K be a field, S = K[x1, . . . ,xn] be the polynomial ring in n variables with coefficient in K and M be a finitely generated Zn-graded S-module. Let u ∈M be a homogeneous element in M and Z a subset of the set of variables {x1, . . . ,xn}. We denote by uK[Z] the K-subspace of M generated by all elements uv where v is a monomial in K[Z]. If uK[Z] is a free K[Z]-module, the Zn-graded K-space ...
متن کاملMonomial ideals of minimal depth
Let S be a polynomial algebra over a field. We study classes of monomial ideals (as for example lexsegment ideals) of S having minimal depth. In particular, Stanley’s conjecture holds for these ideals. Also we show that if I is a monomial ideal with Ass(S/I) = {P1, P2, . . . , Ps} and Pi 6⊂ ∑s 1=j 6=i Pj for all i ∈ [s], then Stanley’s conjecture holds for S/
متن کاملArithmetical rank of squarefree monomial ideals of small arithmetic degree
In this paper, we prove that the arithmetical rank of a squarefree monomial ideal I is equal to the projective dimension of R/I in the following cases: (a) I is an almost complete intersection; (b) arithdeg I = reg I ; (c) arithdeg I = indeg I + 1. We also classify all almost complete intersection squarefree monomial ideals in terms of hypergraphs, and use this classification in the proof in ca...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2009.05.021