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 ${\displaystyle 0+0}$. This property defines one sense in which an additive monoid can be as unlike an additive group as possible: no elements have inverses.

References

• Wehrung, Friedrich (1996). "Tensor products of structures with interpolation". Pacific Journal of Mathematics. 176 (1): 267–285. doi:10.2140/pjm.1996.176.267. Zbl 0865.06010.