Abstract
The definition of p-injectivity motivates us to generalize the notion of injectivity and projectivity, noted respectively C-injectivity and C-projectivity. Noetherian, semi-simple Artinian, quasi-Frobenius, regular hereditary and self-injective regular rings are considered in terms of C-injectivity and C-projectivity. Partial answers are given to Matlis’ Problem and Boyle’s Conjecture.
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