Property: amply supplemented

Definition: For every submodule $N$ of $M$, and every submodule $T$ such that $T+N=M$, there exists a submodule $S$ contained in $T$ minimal with the property that $S+N=M$.


  • R. Wisbauer. Foundations of module and ring theory. (2018) @ Chapter 8 , section 14, subsection 9 p 354


This property has the following metaproperties
  • passes to summands
  • passes to quotients