Exchange PF-rings and almost PP-rings
Recall that a commutative ring R with unity is called PF-ring (respectively PP-ring) if every principal ideal is a flat (respectively projective) R-module. A relation between PF-rings and almost PP-rings is established by proving the following theorems. Theorem 1. Any exchange PF-ring is an almost PP-PM-ring. Theorem 2. Any almost PP-PM-ring is an exchange PF-ring. Theorem 3. Let X be a completely regular Hausdorff space. Then the ring C(X) of all continuous real-valued functions on X is an almost PP-ring if and only if it is a U-ring. Some examples are also given. For instance, the ring of the integers is an almost PP-ring, which is not a PM-ring and so not an exchange ring.
ring of continuous real-valued functions
scientific article; zbMATH DE number 4132304