The ring kernel of a ring homomorphism 
is the set
of all elements of 
which are mapped to the zero element
of 
. It is the group
kernel of 
as a group homomorphism of the underlying additive groups. It is a two-sided
ideal of 
.
Ring Kernel
See also
Group Kernel, Ring HomomorphismThis entry contributed by Margherita Barile
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Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Ring Kernel." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RingKernel.html