Flat modules over group rings of finite groups
Let \(kG\) be the group ring of a finite group \(G\) over a commutative ring \(k\). The author studies the question of existence of a flat \(kG\)-module \(M\) which is projective as \(k\)-module but \(M\) is not projective as \(kG\)-module. He relates this question to the question of existence of a \(k\)-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have \(|k|\geq\aleph_\omega\). Moreover, he proves that there can be no such example if \(k\) is a commutative Noetherian ring with finite Krull dimension, or if \(k\) is a perfect ring.
scientific article; zbMATH DE number 1385254