ON A GENERALIZATION OF TILTING MODULES

Let R be a ring. A right R-module U is called Tor-tilting if Cogen (U+) = Ker Tor(1)(R)(U, -), where U+ = Hom(Z)(U, Q/Z), Cogen (U+) is the class of left R-modules cogenerated by U+ and Ker Tor(1)(R)(U, -) consists of modules M-R such that Tor(1)(R)(U, M) = 0. Some examples and characterizations of Tor-tilting modules are given. Among others, it is shown that U-R is Tor-tilting if and only if U+ is cotilting. Moreover, both tilting modules and completely faithful flat modules are proved to be Tor-tilting. The torsion theory induced by a Tor-tilting module is also investigated.