On coflat modules. I (Q2639135)

This paper follows up the work of \textit{R. F. Damiano} [Pac. J. Math. 81, 349-369 (1979; Zbl 0415.16021)] on coflat modules over a ring R with 1. A module M is coflat if \(Hom_ R(\underline{\;},M)\) is right exact on \(0\to I\to R\). Then R is called FC if R is left and right coherent and both \({}_ RR\) and \(R_ R\) are coflat. If R is FC and P is a finitely generated projective module, then End(P) is also FC; moreover, the following statements are equivalent: (1) \(P_ R\) is an injector, (2) \(P_ R\) is a coflatjector, and (3) \(P_ R\) is a flatjector. Each coflat right R- module is projective if and only if R is quasi-Frobenius. Some other elementary results on coflat modules are also proved.