Zerosumfree monoid

In abstract algebra, an additive monoid $(M,\; 0,\; +)$ is said to be zerosumfree if nonzero elements do not sum to zero. Formally:

:$(forall\; a,bin\; M)\; a\; +\; b\; =\; 0\; implies\; a\; =\; 0\; !$

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