Algebraic Number Theory
《Algebraic Number Theory》 · 第 194 页 · Chapter III，Section 2「Different and Discriminant」，定义段
Let $L/K$ be a finite separable field extension, $\mathfrak o\subset K$ a Dedekind domain with field of fractions $K$, and let $\mathfrak O\subset L$ be its integral closure in $L$. The trace form $T(x,y)=\operatorname{Tr}(xy)$ allows us to associate to every fractional ideal $\mathfrak a$ of $L$ the dual $\mathfrak O$-module $\,{}^*\mathfrak a=\{x\in L\mid\operatorname{Tr}(x\mathfrak a)\subseteq\mathfrak o\}$. It is again a fractional ideal.