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-pure submodules

DOI: 10.1155/ijmms.2005.491

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Abstract:

A submodule A of a right R-module B is called s-pure if f⊗R1S is a monomorphism for every simple left R-module S, where f:A→B is the inclusion homomorphism. We establish some properties of s-pure submodules and use s-purity to characterize commutative rings with every maximal ideal idempotent.

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