There exists a local ring R with a unique prime ideal and a nonzero ideal I ⊂ R which is a flat R-module. See Section Tag 05FZ.

Slogan: Zero dimensional ring with flat ideal.

There exists a local ring R with a unique prime ideal and a nonzero ideal I ⊂ R which is a flat R-module. See Section Tag 05FZ.

Slogan: Zero dimensional ring with flat ideal.