Displaying similar documents to “On presented dimensions of modules and rings.”

Behavior of countably generated pure-projective modules.

Goro Azumaya (1992)

Publicacions Matemàtiques

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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.