Singular submodule

In the context of module theory, the concept of a singular submodule arises when studying modules over a ring in relation to their annihilators. Specifically, given a module \( M \) over a ring \( R \), a submodule \( N \) of \( M \) is called a **singular submodule** if it consists of elements that can be "killed" by some non-zero element of the ring \( R \).