We first prove that every countably presented module is a pure epimorphic image of a countably generated pure-projective module, and by using this we prove that if every countably generated pure-projective module is pure-injective then every module is pure-injective, while if in any countably generated pure-projective module every countably generated pure-projective pure submodule is a direct summand then every module is pure-projective.
@article{urn:eudml:doc:41720,
title = {Behavior of countably generated pure-projective modules.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {401-406},
mrnumber = {MR1209810},
zbl = {0792.16001},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41720}
}
Azumaya, Goro. Behavior of countably generated pure-projective modules.. Publicacions Matemàtiques, Tome 36 (1992) pp. 401-406. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41720/