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 U _S consisting of pseudo-regular S-systems, is constructed. Its corresponding quasi-filter is completely described. A number of results on the relations between τ _u and two special torsion theories, the stable and Lambek torsion theories, are obtained.