A note on indecomposable projective modules
Let R be a commutative ring with unity. All modules are assumed to be unitary R-modules. A module M is said to be finitely related if there exists a short exact sequence of R-modules \(0\to K\to F\to M\to 0\) where F is a free module and K is a finitely generated module. - A module M is said to be hereditarily projective if M is projective and L(M) is a projective ideal for each \(L\in Hom_ R(M,R).\) The author proves: (1) If M is a finitely related projective R-module, then \(M=M_ 1\oplus M_ 2\), where \(M_ 1\) is a finitely generated projective R-module and \(M_ 2\) is a free R-module; \((2)\quad If\) M is a hereditarily projective module which is indecomposable, then M is finitely generated.
scientific article; zbMATH DE number 4128952