Zerosumfree monoid explained

(M,0,+)

is said to be zerosumfree, conical, centerless or positive if nonzero elements do not sum to zero. Formally:

(\foralla,b\inM) a+b=0\impliesa=b=0

This means that the only way zero can be expressed as a sum is as

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.

References

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Zerosumfree monoid".

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