标题： 一个单形分解的族，这些分解是DG-代数 显示英文标题

标题： A family of simplicial resolutions which are DG-algebras

摘要： 每个多项式环上的单项式理想都具有DG代数结构的自由分解，即Taylor分解。 我们引入的单项式理想的pivot分解是一种总是比Taylor分解更短的分解（除非Taylor分解已经是最短的），但仍保留DG代数结构。 我们研究了这一分解族的基本性质，包括构造何时为最小的特征。 根据Sobieska的工作，我们利用pivot分解的明确性，给出在完全交上给定单项式理想自由分解的Eisenbud-Shamash构造的公式。 显示英文摘要

摘要： Each monomial ideal over a polynomial ring admits a free resolution which has the structure of a DG-algebra, namely, the Taylor resolution. A pivot resolution of a monomial ideal, which we introduce, is a resolution that is always shorter than the Taylor resolution (unless the Taylor resolution is as short as possible) but still retains a DG-algebra structure. We study the basic properties of this family of resolutions including a characterization of when the construction is minimal. Following the work of Sobieska, we use the explicit nature of pivot resolutions to give formulae for the Eisenbud-Shamash construction of a free resolution of a given monomial ideal over complete intersections.