Stanley depth of monomial ideals with small number of generators

• Autorzy: Mircea Cimpoeaş
• Języki publikacji: EN

Abstrakty

EN

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 3]//I) +1 for any monomial ideal in I ⊂ K[x 1,x 2,x 3].

Słowa kluczowe

EN

Stanley depth; Monomial ideal

Kategorie tematyczne

• 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 4
• Strony: 629-634

Daty

wydano

2009-12-01

online

2009-10-31

Twórcy

autor

Mircea Cimpoeaş

• Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0037-0