Coproducts of Countably-Generated Modules

Le résumé fourni par la source

In his study of the structure of projective modules, Kaplansky [1958] found that every projective left R-module must be the direct sum of countably-generated submodules. He obtained this fundamental result as a corollary of a theorem that is the subject of the present chapter: the class of coproducts of countably-generated left R-modules is closed under taking direct summands. The present chapter is an exposition of Kaplansky’s proof of this closure property, and the next chapter consists of structural consequences for projective modules that are derived through the use of this closure property.

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