Abstract: The concept of projectively coresolved Gorenstein AC-flat modules is introduced (PGACF-modules for short), and the equivalent condition of these modules is given. Let $\boldsymbol{T}= \left(\begin{array}{ll}A & 0 \\ U & B\end{array}\right)$ be a triangular matrix ring, where A and B are rings, and U is a (B,A)-bimodule. Under some conditions, it is demonstrated $M=\left(\begin{array}{l}M_{1} \\ M_{2}\end{array}\right)_{\varphi^{M}} $ is a PGACF left T-module, then M₁ is a PGACF left A-module, Cokerφ^M is a PGACF left B-module and the morphism φ^M is a monomorphism; if the class of PGACF-modules is closed under extensions, the opposite case holds.

Key words: projectively coresolved Gorenstein AC-flat modules, triangular matrix rings, absolutely clean modules