English

A quasi-additive property of homological shift ideals

Commutative Algebra 2023-10-24 v1

Abstract

In this paper, we investigate which classes of monomial ideals have a quasi-additive property of homological shift ideals. More precisely, for a monomial ideal II we are interested to find out whether HSi+j(I)HSi(HSj(I))HS_{i+j}(I)\subseteq HS_i(HS_j(I)). It turns out that c\mathbf{c}-bounded principal Borel ideals as well as polymatroidal ideals satisfying strong exchange property, and polymatroidal ideals generated in degree two have this quasi-additive property. For squarefree Borel ideals, we even have equality. Besides, the inclusion holds for every equigenerated Borel ideal and polymatroidal ideal when j=1j=1.

Keywords

Cite

@article{arxiv.2310.14247,
  title  = {A quasi-additive property of homological shift ideals},
  author = {Shamila Bayati},
  journal= {arXiv preprint arXiv:2310.14247},
  year   = {2023}
}