On the behavior of adjoint ideals under pure morphisms

We characterize adjoint ideal sheaves via ultraproducts and, utilizing this characterization, study their behavior under pure morphisms. In particular, given a pure morphism $f:Y\to X$ between normal quasi-projective complex varieties, a reduced divisor $D$ and an effective $\mathbb{Q}$-Weil divisor $\mathrm{\Gamma }$ on $X$ without common components, we have the following result: if the cycle-theoretic pullback $E:=f^{\mathrm{♮}}D$ is reduced and $(Y,E+f^{\ast }\mathrm{\Gamma })$ is of plt type along $E$, then $(X,D+\mathrm{\Gamma })$ is of plt type along $D$. This provides an affirmative answer to a question posed by Z. Zhuang.