LAUSR

Abstract Let T = ( A 0 U B ) 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 ( P D 1 C 1 , A D 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 ( A D 1 C 1 , I D 2 C 2 ) is a (resp. hereditary complete) cotorsion pair in T-Mod. In addition, we characterize some special preenveloping classes and precovering classes in T-Mod.