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 $0 + 0$.

References

• Wehrung, Friedrich (1996). "Tensor products of structures with interpolation". Pacific Journal of Mathematics 176 (1): 267–285. Zbl 0865.06010.