Abstract：This paper presents a study on the Ding graded projective (injective) R-modules and strong Ding graded projective (injective) R-modules over a graded ring R. It is proved that the class of the Ding graded projective (injective) modules over any graded ring is projectively (injectively) resoluble.Some characterizations of these modules are discussed. Some relations between strongly Ding graded projective (injective) R-modules and Ding graded projective (injective) R-modules are listed. Finally, the relation between strong Ding graded projective (injective) R-modules and ungraded strong Ding projective (injective) R-modules is also studied. It is proved that for finite group graded ring R, if M is a strong Ding projective (injective) R-modules, then F(M) is a strong Ding graded projective (injective), and if N is a strong Ding graded projective (injective) R-modules, then U(N) is a strong Ding projective (injective).
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2018, Vol. 45 
