Editing Semigroup action (section)

==Examples==
* Any semigroup <math>(S, *)</math> has an action on <math>S</math>, where <math>\cdot = *</math>. The action property holds due to the associativity of <math>*</math>.
* More generally, for any semigroup homomorphism <math>F\colon (S, *) \rightarrow (T, \oplus)</math>, the semigroup <math>(S, *)</math> has an action on <math>T</math> given by <math>s \cdot t = F(s) \oplus t</math>.
* For any set <math>X</math>, let <math>X^*</math> be the set of sequences of elements of <math>X</math>. The semigroup <math>(\mathbb{N}, \times)</math> has an action on <math>X^*</math> given by <math>n \cdot s = s^n</math> (where <math>s^n</math> denotes <math>s</math> repeated <math>n</math> times).
* The semigroup <math>(\mathbb{N}, \times)</math> has a right action <math>(\mathbb{N}, \cdot)</math>, given by <math>x \cdot y = x^y</math>.