Closure Along an Admissible Subset, Seminormality and $T$-Closedness

Abstract

We introduce the closure of an injective ring morphism A → B along an admissible subset X of Spec (A) (an admissible subset X is the spectral image of a flat epimorphism A → E). Then we give a theory of seminormality and t-closedness along admissible subsets which extends Yanagihara's work on S-seminormality.