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. how far is 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.

对于一个数值半群环K [ H ] 我们研究其典型理想的迹。这个理想的共长称为H的余数。这个不变量衡量H离对称有多远，即K [ H ] 离成为 Gorenstein 环有多远。我们注意到规范迹线理想包含导体理想，我们研究了残差的界限。对于 3 生成的数值半群，我们给出了典型迹理想和H的残差的明确公式。因此，在这种情况下，我们可以对残基至多为 1 的那些（接近 Gorenstein 的那些）进行分类，并且我们展示了残基在移位家族中的最终周期性行为。