It is proved that R is Artinian semisimple if and only if there exists a cardinal c , so that every left R module is the direct sum of a direct projective module and a c limted ES module; if and only if there exists a cardinal c , so that every left R module is the direct sum of a direct injective module and a c limted ES module.
证明了环R是Artin半单的当且仅当存在一个基数c,使得任意左R-模是一个直投射模和一个c-限制的ES-模的直和,也当且仅当存在一个基数c,使得任意左R-模是一个直内射模和一个c-限制的ES-模的直
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