A note on Stanley conjecture for monomial ideals

Mircea Cimpoeas

A note on Stanley conjecture for monomial ideals

Commutative Algebra 2011-12-30 v2

Authors: Mircea Cimpoeas

Abstract

In this paper, we prove that if $I\subset S:=K[x_1,...,x_n]$ is a monomial ideal then $I$ and $S/I$ satisfy the Stanley conjecture when $I$ has a small number of generators, with respect to $\depth(S/I)$ and $\max\{|P|:\;P\in\Ass(S/I)\}$ . In particular, if $I$ be a monomial almost complete intersection ideal in $S$ , then Stanley's Conjecture holds for $S/I$ and $I$ .

Keywords

monomial ideals monomial ideals and free resolutions ideal theory

Cite

@article{arxiv.1111.1550,
  title  = {A note on Stanley conjecture for monomial ideals},
  author = {Mircea Cimpoeas},
  journal= {arXiv preprint arXiv:1111.1550},
  year   = {2011}
}

Comments

This paper was withdrawn because it was accepted to be published in Bull. Math. Soc. Roumanie with the title changed in "The Stanley conjecture on monomial almost complete intersection ideals". One can find the new version of the paper on Arxiv:1112.4956

A note on Stanley conjecture for monomial ideals

Abstract

Keywords

Cite

Comments

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