标题： Stanley-Reisner 环在去心谱上为 Gorenstein 的规范迹 显示英文标题

标题： The canonical trace of Stanley-Reisner rings that are Gorenstein on the punctured spectrum

摘要： 在本文中，我们证明了至少3维的几乎Gorenstein Stanley-Reisner环确实是Gorenstein。 通过第一作者之前的成果，这得到了几乎Gorenstein Stanley-Reisner环的完整刻画。 我们还表明，一个Cohen-Macaulay Stanley-Reisner环在去掉原点的谱上是Gorenstein当且仅当它几乎是Gorenstein或者其典范迹是其无关极大理想的平方，并且后一种情况恰好出现在非可定向的同调流形上。 显示英文摘要

摘要： In this paper we prove that nearly Gorenstein Stanley-Reisner rings of dimension at least 3 are indeed Gorenstein. By previous work of the first author this yields a complete characterization of nearly Gorenstein Stanley-Reisner rings. We also show that a Cohen-Macaulay Stanley-Reisner ring is Gorenstein on the punctured spectrum if and only if either it is nearly Gorenstein or its canonical trace is the square of its irrelevant maximal ideal, and that the latter case happens exactly for non-orientable homology manifolds.