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