Displaying similar documents to “On the Betti numbers of perfect ideals”

Fiber cones and the integral closure of ideals.

R. Hübl, C. Huneke (2001)

Collectanea Mathematica

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Let (R,m) be a Noetherian local ring and let I C R be an ideal. This paper studies the question of when m I is integrally closed. Particular attention is focused on the case R is a regular local ring and I is a reduced ideal. This question arose through a question posed by Eisenbud and Mazur on the existence of evolutions.

Stanley depth of monomial ideals with small number of generators

Mircea Cimpoeaş (2009)

Open Mathematics

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For 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...