Behavior of countably generated pure-projective modules
Copyright policy )Behavior of countably generated pure-projective modules
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 show 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.
left pure-semisimple rings, Injective modules, self-injective associative rings, indecomposable submodules, Free, projective, and flat modules and ideals in associative algebras, countably presented left \(R\)-module, Simple and semisimple modules, primitive rings and ideals in associative algebras, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), countably generated pure-projective modules, direct summand, short exact sequence, pure submodule, left \(R\)-modules, finitely generated submodules
left pure-semisimple rings, Injective modules, self-injective associative rings, indecomposable submodules, Free, projective, and flat modules and ideals in associative algebras, countably presented left \(R\)-module, Simple and semisimple modules, primitive rings and ideals in associative algebras, Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras), countably generated pure-projective modules, direct summand, short exact sequence, pure submodule, left \(R\)-modules, finitely generated submodules
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