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