… Next, we determine the structures of C-pure projective modules over a left Artinian ring. We
… a left R-module M is C-pure projective if and only if it is a direct sum of cyclic modules (see …

… module is a direct sum of a projective module and a semisimple … C-flat modules coincide with
singly-projective modules over … to singly projective modules in terms of C-pure submodules. …

… projective property with respect to all pure (C-pure) exact sequences. Pure projective modules
and C-pure projective modules … neat projective module is a direct sum of a projective and …

… A ring R is called left hereditary if every left ideal of R is projective. Since pure-projective
modules and FP-projective modules are generalizations of … C-pure projective modules …

… only if every cyclic left R-module is pure-projective. As a corollary of this result … -pure-injective
as an R-module, since any direct sum of projective modules is … C-pure projective modules …

… With respect to purity, flat, absolutely pure and regular modules … c-pure and c-regular modules
for cyclic purity. We prove that absolutely c-pure R-modules are precisely injective modules…

… Thus every projective module is finitely projective, and every finitely projective module is flat…
and only if f is C-pure, and this is also equivalent to the condition that f is M-pure for all left R-…

… We study direct-sum decompositions of RD-projective modules over some classes of
rings. … RD-projective right module is a direct sum of cyclically presented right modules (Proposition …

… taking C ∈ A(R−mod) we define the C-pure sequences of left Rmodules, C-projective left
R-… projective modules share some convenient properties with the usual projective modules. …

… In model theory the notions of pure-injective modules and pure-projective modules are
more useful than that of injective modules and projective modules. These modules have been …