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.