Zerosumfree monoid

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


 * $$(\forall a,b\in M)\ a + b = 0 \implies a = b = 0 \!$$

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