… R these modules form a torsionfree class for a torsion theory if and only if R, is … Rmodules
have covers by submodules of flat R-modules if and only if all injective left R-modules have flat …

… if for every submodule N of M, there exists an ideal B of the … A module MA is said to be flat if
for every left A-module L, the … If all submodules of any right or left module over a ring A are flat…

… Such a generalization is the next definition, but before recall that if T is a hereditary torsion
theory in the category of left R-modules, M is a left R-module and N is a submodule of M, the …

… theG-spaceX only has good properties ifA is left (or right) faithfully flat as a module overB. …
as a left or rightB-module is faithfully flat. Moreover, the coalgebraA/AB + is cosemisimple. …

… jective and flat modules over group rings. We begin with a general theorem about flat modules
over an … of M is contained in a countably generated submodule K of M such that P/K is flat. …

… over which al.1 submodules of flat right modules and fiat left modules are flat; … module M
is flat iff any cyclic submodule of the module M is contained in a flat submodule of the module …

… submodules, and the lattice of all submodules of a module M, … A submodule HE Lat(M) is
closed in M if H has no proper … submodule of a flat module PA, and the factor module P/Q is …

… Assume that each Si is a submodule of a flat module Fi. Let Ω be the set of the flat
modules Fi. Set F := … A module MR has a nonzero i-test submodule if and only if M is i-test. …

… finitely generated submodules Mj and M2 of some module, it follows that Afj f| M2 is finitely
generated if Mi + M2 is finitely presented. The following lemma can be immediately derived …

… of rings and modules via C-purity are considered. We prove that every C-flat module is
injective if … , we show that R is a CF ring if and only if every FP-injective right R-module is C-flat. …