Splitting ring extensions

The paper deals with ring extensions $$R\subseteq S$$ and their lattices [R, S] of subextensions is mainly devoted to FCP (extensions whose are Artinian Noetherian). object the introduction study elements that split in some sense extensions. reason why this splitting was used earlier without common nature being recognized. There favorable cases allowing build splitters, when we dealing $${\mathcal {B}}$$ -extensions, for example integral Integral closures Prüfer hulls play a dual role. gives many combinatorics results explicit computation hull an extension. We show extension cannot be pinched, except trivially.