Abstract: Let T be a formal triangular matrix ring. First, this paper investigates clean-projective modules over T, and proves that if a left T-module (X,Y)_φ is clean-projective, then X/(Im φ) is a clean-projective left R-module and Y is a clean-projective left S-module. Second, the recollements for clean-derived categories and clean-singularity categories over T are constructed separately.

Key words: formal triangular matrix ring, clean-projective module, clean-singularity category, recollement