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\$.