Resumen de When is each proper overring of R an S (Eidenberg) domain?

Noôman Jarboui

• A domain $R$ is called a maximal "non-S" subring of a field $L$ if $R\subset L$, $R$ is not an S-domain and each domain $T$ such that $R\subset T\subseteq L$ is an S-domain. We show that maximal "non-S" subrings $R$ of a field $L$ are the integrally closed pseudo-valuation domains satisfying $\dim(R) = 1$, $\dim_v(R) = 2$ and $L= \operatorname{qf}(R)$.