Displaying similar documents to “Modules which are epi-equivalent to projective modules”

Characterizations of semiperfect and perfect rings.

Weimin Xue (1996)

Publicacions Matemàtiques

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We characterize semiperfect modules, semiperfect rings, and perfect rings using locally projective covers and generalized locally projective covers, where locally projective modules were introduced by Zimmermann-Huisgen and generalized locally projective covers are adapted from Azumaya’s generalized projective covers.

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.