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.

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