On the behavior of adjoint ideals under pure morphisms

We characterize adjoint ideal sheaves via ultraproducts and study their behavior under pure morphisms by utilizing this characterization. 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 \Gamma on X with no common components, we have the following result: if the cycle-theoretic pullback E:=f^{\natural}D is reduced and (Y, E+f^{*}\Gamma) is of plt type along E , then (X, D+\Gamma) is of plt type along D . This provides an affirmative answer to a question posed by Z. Zhuang [Invent. Math. 237 (2024)].