zerosumfree monoid

{{Short description|Concept in abstract algebra}}

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:

:$(\backslash forall\; a,b\backslash in\; M)\backslash \; a\; +\; b\; =\; 0\; \backslash implies\; a\; =\; b\; =\; 0\; \backslash !$

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.