Small Submodule
A submodule S of a module M such that for any proper submodule T of M, the submodule generated by S union T is not the entire module M. S is also called superfluous submodule.
See also
Large Submodule, SubmoduleThis entry contributed by Margherita Barile
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Barile, Margherita. "Small Submodule." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SmallSubmodule.html