# Behavior of countably generated pure-projective modules.

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 2A, page 401-406
- ISSN: 0214-1493

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topAzumaya, Goro. "Behavior of countably generated pure-projective modules.." Publicacions Matemàtiques 36.2A (1992): 401-406. <http://eudml.org/doc/41720>.

@article{Azumaya1992,

abstract = {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.},

author = {Azumaya, Goro},

journal = {Publicacions Matemàtiques},

keywords = {short exact sequence; left -modules; pure submodule; finitely generated submodules; indecomposable submodules; left pure-semisimple rings; countably generated pure-projective modules; countably presented left -module; direct summand},

language = {eng},

number = {2A},

pages = {401-406},

title = {Behavior of countably generated pure-projective modules.},

url = {http://eudml.org/doc/41720},

volume = {36},

year = {1992},

}

TY - JOUR

AU - Azumaya, Goro

TI - Behavior of countably generated pure-projective modules.

JO - Publicacions Matemàtiques

PY - 1992

VL - 36

IS - 2A

SP - 401

EP - 406

AB - 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.

LA - eng

KW - short exact sequence; left -modules; pure submodule; finitely generated submodules; indecomposable submodules; left pure-semisimple rings; countably generated pure-projective modules; countably presented left -module; direct summand

UR - http://eudml.org/doc/41720

ER -