Campillo, AntonioCastellanos Peñuela, Julio Antonio2023-06-202023-06-2020020025-587410.1007/s002090100343https://hdl.handle.net/20.500.14352/58358We consider complete ideals supported on finite sequences of infinitely near points, in regular local rings with dimensions greater than two. We study properties of factorizations in Lipman special *-simple complete ideals. We relate it to a type of proximity, linear proximity, of the points, and give conditions in order to have unique factorization. Several examples are presented.engjournal articlehttp://link.springer.com/content/pdf/10.1007%2Fs002090100343http://www.springer.comrestricted access512Regular local ringsÁlgebra1201 Álgebra