Zerosumfree monoid explained

(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

• Tensor products of structures with interpolation. Friedrich . Wehrung. Pacific Journal of Mathematics. 176. 1. 1996. 267 - 285 . 10.2140/pjm.1996.176.267 . 0865.06010 . free.