CLOSURE ALONG AN ADMISSIBLE
SUBSET, SEMINORMALITY
AND $T$-CLOSEDNESS

GABRIEL PICAVET AND
MARTINE PICAVET-L'HERMITTE

Abstract:

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