View source for 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 $L = M$.

See also: [[Essential subgroup]].

====References====
* F.W. Anderson, K.R. Fuller, "Rings and Categories of Modules" Graduate Texts in Mathematics '''13''' Springer (2012) ISBN 1468499130