Zerosumfree monoid

In abstract algebra, an additive monoid ${\displaystyle (M,0,+)}$ is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally:

${\displaystyle (\forall a,b\in M)\ a+b=0\implies a=b=0\!}$

This means that the only way zero can be expressed as a sum is as ${\displaystyle 0+0}$.