Torsionfree classes and precovers
by
Ladislav Bican
KA MFF UK, Sokolovska 83, 186 00 Praha 8-Karlin, CZ

Let t = (T, F) be an exact hereditary torsion theory for the category R-mod of left unitary modules over an associative ring with the identity element. The class F is a cover (precover) class if and only if the classes of relatively exact or torsionfree relatively injective modules are cover (precover) classes. These conditions are satisfied if and only if t is of finite type, which leads to an example of a hereditary torsion theory where the torsionfree class is not a precover class. A new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie's torsion theory is described.

Date received: April 28, 2004