Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.4145

Stanley decompositions of squarefree modules and Alexander duality

Ali Soleyman Jahan
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper we study how prime filtrations and squarefree Stanley decompositions of squarefree modules over the polynomial ring and the exterior algebra behave with respect to Alexander duality.

Explore related subjects

math.ACmath.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ali Soleyman Jahan. 2007-09-26. Stanley decompositions of squarefree modules and Alexander duality. https://arxiv.org/abs/0709.4145

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Homological subsets of Spec

We recover some data of a module $M$ from the Ext-family $\{Ext^i_R(M,R)\}$. In this regard, we investigate homological subsets of $Spec(R)$, defined by the help of Ext-family. For example, we present a situation for which $\bigcup_{i=0}^\infty Ass(Ext^i_R(M,R))$ is infinite, thereby answering a question of Vasconcelos. We extend Grothendieck's calculation of $dim(Ext^g_R(M,R))$ and present some new situations to calculate $dim(Ext^\ast_R(M,R))$. Also, we compute support and the set of all associated prime ideals of the Ext-family in a serial of nontrivial cases.

math.AC↗
arXiv2026

On Stanley-Reisner Rings with Minimal Betti Numbers

We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal sum of Betti numbers. We prove that every full subcomplex of them is homotopy equivalent either to a point or to a sphere. Moreover, we prove that such kind of simplicial complexes coincide with those having minimal Taylor resolutions.

math.AC↗
arXiv2026

Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions

For every pair of integers $d,n\geq1$, we construct a commutative noetherian local-Cohen-Macaulay DG-ring $A$ such that $\dim H^0(A)=d$, $\mathrm{amp}(A)=n$, $\mathrm{fpd}(A)=d-n$, and $\mathrm{FPD}(A)=d$. This gives a negative answer to the implication from local-Cohen-Macaulayness to equality of the two finitistic projective dimensions in a question of Bird, Shaul, Sridhar, and Williamson.

math.AC↗