Example of zero symmetric part of near-ring can you help me to find the example of zero symmetric of near ring?
A left near-ring N is called Zero symmetric
if 0x = 0 for all x element N

If you take a nonabelian group $G$ and let $N$ be the nearring of functions from $G$ into $G$ with pointwise addition and function composition as operations, you will be close.
The zero map already absorbs on the right ($0\circ f=0$) but not necessarily on the left. But it turns out that the subset $\{g\in N\mid g\circ 0=0\}$ is a subnearring of $N$ that is zero symmetric. Pick your favorite small nonabelian groups and see which ones yield a nontrivial subnearring of this type.
