PERIODIC FLAT MODULES, AND FLAT MODULES FOR FINITE GROUPS

The main theorem says that if R is a ring of coeecients and G a nite group, then a at RG-module M which is projective as an R-module is necessarily projective as an RG-module. This is proved using the following theorem about at modules over an arbitrary ring R. If a at R-module M sits in a short exact sequence 0 ! M ! P ! M ! 0 with P projective, then M is projective.