论文标题
数值半群环的规范跟踪理想和残留物
Canonical trace ideal and residue for numerical semigroup rings
论文作者
论文摘要
对于数值半群环$ k [h] $，我们研究其规范理想的痕迹。该理想的colength称为$ h $的残留物。这种不变的方法可以衡量与对称的$ h $相距$ h $的距离，即$ k [h] $距成为戈伦斯坦戒指。我们指出，规范轨迹理想包含导体理想，我们研究了残基的界限。 对于$ 3 $生成的数值半群，我们为规范痕迹理想和$ h $的残留物提供了明确的公式。因此，在这种情况下，我们可以对那些最多是残留物（几乎是戈伦斯坦的残留物）进行分类，并且我们显示了在转移家庭中残留物的最终周期性行为。
For a numerical semigroup ring $K[H]$ we study the trace of its canonical ideal. The colength of this ideal is called the residue of $H$. This invariant measures how far is $H$ from being symmetric, i.e. $K[H]$ from being a Gorenstein ring. We remark that the canonical trace ideal contains the conductor ideal, and we study bounds for the residue. For $3$-generated numerical semigroups we give explicit formulas for the canonical trace ideal and the residue of $H$. Thus, in this setting we can classify those whose residue is at most one (the nearly-Gorenstein ones), and we show the eventual periodic behaviour of the residue in a shifted family.
