Hereditary torsion theory of pseudo-regular S-systems

The concept of pseudo-regular S-system is introduced. A torsion theory \(\tau _u = \left( {U_S ,\bar U_S } \right)\) with its torsion class US consisting of pseudo-regular S-systems, is constructed. Its corresponding quasi-filter is completely described. A number of results on the relations between τu and two special torsion theories, the stable and Lambek torsion theories, are obtained.