Stanley depth on five generated, squarefree, monomial ideals

zbMATH Open1363.13009arXiv1312.0923MaRDI QIDQ5298653

Dorin Popescu

Publication date: 15 December 2016

Abstract: Let $IsupsetneqJ$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $geqd$, resp. $geqd+1$ . Suppose that $I$ is either generated by four squarefree monomials of degrees $d$ and others of degrees $geqd+1$, or by five special monomials of degrees $d$. If the Stanley depth of $I/J$ is $leqd+1$ then the usual depth of $I/J$ is $leqd+1$ too.

Full work available at URL: https://arxiv.org/abs/1312.0923

zbMATH Keywords

depthmonomial idealsStanley depth

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

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