Abstract: Let T=A0 UB be a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule. Equivalent characterizations of left T-modules of finite cogeneration and finite corepresentation on the formal triangular matrix ring are given. Furthermore, a characterization of FC-projective left T-modules over the formal triangular matrix ring is given. As an application, the FC-projective dimensions of left T-modules are discussed.

Key words: FC-projective module, co-noetherian ring, FC-projective dimension