Abstract Let T=(A 0 UB) be a formal triangular matrix ring, where A and B are rings and U is
a (B, A)-bimodule. Let C 1 and C 2 be two classes of left A-modules, D 1 and D 2 be two
classes of left B-modules, we prove that:(1) If Tor i A (U, C 1)= 0 for any i≥ 1,(C 1, C 2) and
(D 1, D 2) are (resp. hereditary complete) cotorsion pairs, then (PD 1 C 1, AD 2 C 2) is a
(resp. hereditary complete) cotorsion pair in T-Mod.(2) If Ext B i (U, D 2)= 0 for any i≥ 1,(C 1,
C 2) and (D 1, D 2) are (resp. hereditary complete) cotorsion pairs, then (AD 1 C 1, ID 2 C 2) …