abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...

, an additive

monoid In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being . Monoids are semigroups with identity ...

(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

. This property defines one sense in which an additive monoid can be as unlike an additive

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...

as possible: no elements have inverses.

References

* Semigroup theory {{Abstract-algebra-stub