Zerosumfree monoid

In abstract algebra, an additive monoid [math]\displaystyle{ (M, 0, +) }[/math] is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally:

[math]\displaystyle{ (\forall a,b\in M)\ a + b = 0 \implies a = b = 0 \! }[/math]

This means that the only way zero can be expressed as a sum is as [math]\displaystyle{ 0 + 0 }[/math].