So it turns out I can’t get rid of this damn radical in my theorem, so it’s more like a proposition now. I have to replace “factorial” with “prefactorial” (i.e. every prime ideal of height one is a radical of a principal ideal). The trouble is, very few people know what prefactorial is, and I have no clue how large the class of germs of varieties with being normal and prefactorial is. It seems to be larger than factorial and smaller than normal.

That’s the problem with ideals and radicals. Just like in politics, they just cause problems. And just like in politics, if you could find the generators of those radical ideals, you could really solve some problems.