Category:Powers (Abstract Algebra)

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This category contains results about Powers (Abstract Algebra).
Definitions specific to this category can be found in Definitions/Powers (Abstract Algebra).

Let $\struct {S, \circ}$ be a magma which has no identity element.

Let $a \in S$.

Let the mapping $\circ^n a: \N_{>0} \to S$ be recursively defined as:

$\forall n \in \N_{>0}: \circ^n a = \begin{cases}

a & : n = 1 \\ \paren {\circ^r a} \circ a & : n = r + 1 \end{cases}$

The mapping $\circ^n a$ is known as the $n$th power of $a$ (under $\circ$).