On traces of exterior powers of a sum of two endomorphisms of a projective module
S. Balcerzyk (1971)
Colloquium Mathematicae
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S. Balcerzyk (1971)
Colloquium Mathematicae
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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.
Zhou, Dexu, Gong, Zhiwei (2010)
International Journal of Mathematics and Mathematical Sciences
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Josef Jirásko (1979)
Commentationes Mathematicae Universitatis Carolinae
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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.