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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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