Stanley depth and size of a monomial ideal
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 I be a monomial squarefree ideal of a polynomial ring S over a field K such that the sum of every three different ideals of its minimal prime ideals is the maximal ideal of S, or more generally a constant ideal. We associate to I a graph on [s], s = |MinS/I|, on which we may read the depth of I. In particular, depthS I does not depend on char K. Also we show that I satisfies Stanley’s Conje...
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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 K be a field and S = K[x1, . . . , xn] be the polynomial ring in n variables over the field K. Let G be a forest with p connected components G1, . . . , Gp and let I = I(G) be its edge ideal in S. Suppose that di is the diameter of Gi, 1 ≤ i ≤ p, and consider d = max{di | 1 ≤ i ≤ p}. Morey has shown that for every t ≥ 1, the quantity max{ d−t+2 3 + p − 1, p} is a lower bound for depth(S/It)...
متن کاملA Survey on Stanley Depth
At the MONICA conference “MONomial Ideals, Computations and Applications” at the CIEM, Castro Urdiales (Cantabria, Spain) in July 2011, I gave three lectures covering different topics of Combinatorial Commutative Algebra: (1) A survey on Stanley decompositions. (2) Generalized Hibi rings and Hibi ideals. (3) Ideals generated by two-minors with applications to Algebraic Statistics. In this artic...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11160-2