Révêtements étales
Ring extensions with some finiteness conditions on the set of intermediate rings
A ring extension is said to be FO if it has only finitely many intermediate rings. is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair...
Rings with an almost Noetherian ring of fractions.