Definition:Power of Element/Notation/Semigroup

Notation for Power of Element of Semigroup
Let $\left({S, \oplus}\right)$ be a semigroup.

Let $a \in S$.

When the operation is addition of numbers or another commutative operation derived from addition, the following symbology is often used:


 * $n a = \begin{cases}

a & : n = 1 \\ \left({n - 1}\right) a + a & : n > 1 \end{cases}$

Sometimes, for clarity, $n \cdot a$ is preferred to $n a$.