Semisimple module

In the context of module theory and representation theory in algebra, a **semisimple module** is a specific type of module that has a particular structure. A module \( M \) over a ring \( R \) is said to be **semisimple** if it satisfies the following equivalent conditions: 1. **Direct Sum Decomposition**: \( M \) can be expressed as a direct sum of simple modules.