The subset 
of a ring. It trivially fulfils the definition of ideal
since it is a group (specifically, the zero group),
and it is closed under multiplication by any element of the ring.
Zero Ideal
See also
Ideal, Proper Ideal, Trivial Ring, Zero Group, Zero ModuleThis entry contributed by Margherita Barile
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Cite this as:
Barile, Margherita. "Zero Ideal." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ZeroIdeal.html