Zerosumfree monoid

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} .

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.


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