Let $ A $ and $ B $ be rings and $ U $ be a $(B, A) $-bimodule. If $ _BU $ has finite flat
dimension, $ U_A $ has finite flat dimension and $\tpa {U}{C} $ is a cotorsion left $ B $-
module for any cotorsion left $ A $-module $ C $, then the Gorenstein flat-cotorsion modules
over the formal triangular matrix ring $ T=\left (\begin {smallmatrix} A & 0\\U & B\\\end
{smallmatrix}\right) $ are explicitly described. As an application, it is proven that each
Gorenstein flat-cotorsion left $ T $-module is flat-cotorsion if and only if every Gorenstein flat …