Hiroshima Math. J. 37 (3), 385-395, (November 2007) DOI: 10.32917/hmj/1200529809
KEYWORDS: C-injectivity, C-projectivity, P-injectivity, von Neumann regular, hereditary, semi-simple Artinian, 16D40, 16D50, 16E50, 16P20, 16P40
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.