zerosumfree monoid
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In
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...
, an additive
monoid In abstract algebra, a branch of mathematics, 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 0. Monoid ...
(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

* Semigroup theory {{Abstract-algebra-stub