Abstract: Let T=((A 0 U B)) be a triangular matrix ring, where A and B are rings and U is a (B,A)-bimodule. We use the isomorphism of modules tensor on the ring T as a bridge to give the equivalent condition that a module on the ring T is a projectively coresolved Gorenstein flat module: if fd(_BU)<∞,fd(U_A)<∞ or id(U_A)<∞, then a left T-module M=((M₁ M₂))_φ^M is projectively coresolved Gorenstein flat module if and only if M₁ is projectively coresolved Gorenstein flat left A-module, Coker φ^M=M₂/Im(φ^M) is projectively coresolved Gorenstein flat left B-module and φ^M: U*_AM₁→M₂ is a monomorphism.

Key words: projectly coresolved Gorenstein flat module, triangular matrix ring, adjoint functor