A semigroup is a set with an associative operation. Adding any two positive integers results in another positive integer; hence, addition is an associative property for natural numbers.
Another example is a monoid with a unit morphism that acts as the identity operator. For example, the set of natural numbers and multiplication morphisms, whose unit morphism is the mutliplyByOne function, or the set of natural numbers and addition morphisms, whose unit morphism is the addZero function.