Number Fields
《Number Fields》 · 第 64 页 · Chapter 3，Exercises 33–39，Exercise 33(c)
Let $A$ be an additive subgroup of $L$. Define $A^{-1}=\{\alpha\in L:\alpha A\subset S\}$, $A^*=\{\alpha\in L:T_{L/K}(\alpha A)\subset R\}$. […] Define the different $\operatorname{diff}A$ to be $(A^*)^{-1}$.