Closed classes of left-$\Lambda$ modules and closed sets of left ideals of ring $\Lambda$

The paper considers classes of $\Lambda$-modules which are completely described by the set of annihilators of the elements of the modules of these classes. A number of conditions on such classes are translated into the language of left ideals. The connections found between classes of $\Lambda$-modules and sets of left ideals of ring $\Lambda$ are used for the characteristics of classes of $\Lambda$-modules related to the concept of torsion.