We introduce and study the set of radical semistar operations an integral domain D. show that their is a complete lattice join-completion spectral operations, we characterize when every operation (under hypothesis D rad-colon coherent). When Prüfer such minimal prime ideals scattered, completely classify stable operations.

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 $${\math...