Generation of proper classes of short exact sequences

Abstract

The generation of proper classes of short exact sequences of modules by subclasses is considered. The class generated by two proper classes is studied by means of some operations between these classes. These operations are investigated in details for classes of short quasi-splitting, torsion-splitting and pure exact sequences of abelian groups.

Keywords

• proper class of short exact sequences
• generated proper class
• coprojectively (coinjectively) generated class
• sum of proper classes
• quasi-splitting (pure
• torsion splitting) short exact sequences
• cotorsion groups
• Ulm's subgroup.