Co-Kasch and Co-polyform Abelian Groups

A submodule N is a co-rational submodule of M provided that Hom ( M , N / L ) = 0 where L is an arbitrary submodule of N . We call a module co-Kasch if it has no non-zero co-rational submodule. In this paper, among other things, we characterize co-Kasch Z -modules and co-polyform Z -modules (i.e., those modules in which every small submodule is co-rational). We also characterize retractable, monoform and epiform Z -modules.