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An example of a uniserial module MR of composition length 2, such that S = End( MR ) acting on the left is not right artinian, is given. An elementary proof of a known result, that the ring of endomorphism of a finite length quasi-injective module MR acting on the left is left artinian, is also given.doi:10.2307/2045373 fatcat:cokulb6rojetbass5ewzf237ve