Behavior of countably generated pure-projective modules.

Goro Azumaya

Publicacions Matemàtiques (1992)

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

Abstract

top
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.

How to cite

top

Azumaya, 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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.