Zerosumfree monoid

Template:Short description 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:

$(\mathrm{\forall }a,b\in M)a+b=0⟹a=b=0$

This means that the only way zero can be expressed as a sum is as $0+0$. This property defines one sense in which an additive monoid can be as unlike an additive group as possible: no elements have inverses.

References

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