On Strongly Affine Extensions of Commutative Rings

A ring extension R subset of S is said to be strongly affine if each R-subalgebra of S is a finite-type R-algebra. In this paper, several characterizations of strongly affine extensions are given. For instance, we establish that if R is a quasi-local ring of finite dimension, then R subset of S is integrally closed and strongly affine if and only if R subset of S is a Prufer extension (i.e. (R, S) is a normal pair). As a consequence, the equivalence of strongly affine extensions, quasi-Prufer extensions and INC-pairs is shown. Let G be a subgroup of the automorphism group of S such that R is invariant under action by G. If R subset of S is strongly affine, then R-G subset of S-G is strongly affine under some conditions.