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Abstract The main objective of this thesis is twofold. First, we aim to study some extended injectivities of graded modules, such as F-injectivity, P- injectivity, and mininjectivity. Second, we aim to investigate the structure of graded quasi-Frobenius rings. Actually, we provide characterizations of graded quasi-Frobenius rings in terms of extended graded injectivities of graded rings. i |