Schwach-Flache Moduln

Abstract

Let R be a commutative, noetherian ring, and let M be an R-module. M is called weakly flat if the kernel of any epimorphism Y ↠ M is closed in Y. Equivalently, a consequence of M/U being singular is that U is essential in M, or that Ann R(𝔭)·M is essential in Ann M(𝔭) for all 𝔭 ∈AssR(M). For a series of important module classes we give an explicit description of their weakly flat objects, and in the local case we investigate the connection between the weak flatness of M and the weak injectivity of the Matlis dual M°. Finally, we characterize those rings R over which every weakly flat R-module is already flat.