A ring homomorphism is said to be pure if its all base changes are injective. For example, split injectives and faithfully flat morphisms are pure. It is natural to ask what singularities descend under pure morphisms. Boutot showed that rational singularities descend under pure morphisms. Recently, Godfrey and Murayama showed the case of Du Bois singularities, and Zhuang showed the case of singularities of klt type and plt type. In this talk, we prove a behavior of adjoint ideals under pure morphisms, which is a generalization of Zhuang’s result. To prove the main theorem, we use Schoutens’ ultraproduct method and the theory of divisorial test ideals. This talk is based on joint work with Shunsuke Takagi.