# Essential submodule

of a module $M$

A submodule $E$ of $M$ is essential it has a non-trival intersection with every non-trivial submodule of $M$: that is, $E \cap L = 0$ implies $L = 0$.

Dually, a submodule $S$ is superfluous if it is not a summand of $M$: that is, $S + L = M$ implies $L = M$.