On a Generalization of Tilting Modules

Abstract

Let R be a ring. A right R-module U is called Tor-tilting if , where U + = Homℤ(U, ℚ/ℤ), Cogen(U +) is the class of left R-modules cogenerated by U + and consists of modules R M such that . 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.