A zero map between two additive groups (or rings, or modules, or vector spaces)
and 
is the map 
such that 
for all 
. It is a homomorphism
in the category of groups
(or rings or modules or vector
spaces).
Zero Map
See also
Constant Map, Identity Map, Zero MorphismThis entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Zero Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ZeroMap.html