An essential submodule 
of a module 
is a submodule having nonzero
intersection with every nonzero submodule
of 
.
Equivalently, every nonzero element of 
has a nonzero scalar multiple in 
. Essential extensions are central in the construction of injective
hulls.
Essential Submodule
See also
Injective Module, Module, SubmoduleExplore with Wolfram|Alpha
References
Lam, T. Y. Lectures on Modules and Rings. New York: Springer-Verlag, 1999.Cite this as:
Weisstein, Eric W. "Essential Submodule." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EssentialSubmodule.html