Zerosumfree monoid
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In abstract algebra, an additive monoid ( M , 0 , + ) {\displaystyle (M,0,+)} is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally:
( ∀ a , b ∈ M ) a + b = 0 ⟹ a = b = 0 {\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 0 + 0 {\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.