Stanley depth of edge ideals
نویسندگان
چکیده
منابع مشابه
Stanley 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...
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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...
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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 ...
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Let G be a finite graph on the vertex set [d] = {1, . . . , d} with the edges e1, . . . , en and K[t] = K[t1, . . . , td] the polynomial ring in d variables over a field K. The edge ring of G is the semigroup ringK[G] which is generated by those monomials t = titj such that e = {i, j} is an edge of G. Let K[x] = K[x1, . . . , xn] be the polynomial ring in n variables over K and define the surje...
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We answer positively a question of Asia Rauf for the case of intersections of three prime ideals generated by disjoint sets of variables and we present several inequalities on Stanley depth. This is a detailed presentation of our talk at the conference on ”Fundamental structures of algebra” in honor of Prof. Serban Basarab at his 70-th anniversary. Let S = K[x1, . . . , xn] be a polynomial alge...
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ژورنال
عنوان ژورنال: Studia Scientiarum Mathematicarum Hungarica
سال: 2012
ISSN: 0081-6906,1588-2896
DOI: 10.1556/sscmath.49.2012.4.1223