All the necessary definitions are given in the introduction. Since it is not true that every left R-module possesses a projective cover, as is the case with injective hulls, it is the aim of this paper to consider a weakened form of a projective cover. In section 2 the concept of a weakly-projective cover is defined and developed. In section 3 this concept is compared with that of a quasi-projective cover. For example it is shown that in the case where a quasi-projective cover can he obtained from an existing projective cover, this quasi-projective cover is nothing more than a weakly-projective cover [Theorem 3.4].
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