论文标题
残留场的最小自由分辨率的截断
A truncated minimal free resolution of the residue field
论文作者
论文摘要
在1962年的一篇论文中，戈洛德证明了局部环的残基场的贝蒂序列达到了塞雷的上限，并且只有当时该环的Koszul复合物的同源代数具有琐碎的乘法和琐碎的Massey操作。这是Golod环的概念的起源。他使用Koszul复合物成分，他还构建了残留场的最小游离分辨率。在本文中，我们将此构造延长至5度，以供任何本地戒指。我们描述了Koszul代数的同源性的乘法结构和三重梅西产品如何参与这种结构。结果，我们为序列的前六个术语提供明确的公式，该序列是测量环与Golod有多远的序列。
In a paper in 1962, Golod proved that the Betti sequence of the residue field of a local ring attains an upper bound given by Serre if and only if the homology algebra of the Koszul complex of the ring has trivial multiplications and trivial Massey operations. This is the origin of the notion of Golod ring. Using the Koszul complex components he also constructed a minimal free resolution of the residue field. In this article, we extend this construction up to degree five for any local ring. We describe how the multiplicative structure and the triple Massey products of the homology of the Koszul algebra are involved in this construction. As a consequence, we provide explicit formulas for the first six terms of a sequence that measures how far the ring is from being Golod.
