Category:Definitions/Powers (Abstract Algebra)
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This category contains definitions related to Powers (Abstract Algebra).
Related results can be found in Category: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 $\circ$).
Pages in category "Definitions/Powers (Abstract Algebra)"
The following 9 pages are in this category, out of 9 total.
P
- Definition:Power Associativity
- Definition:Power of Element
- Definition:Power of Element/Also defined as
- Definition:Power of Element/Field
- Definition:Power of Element/Magma
- Definition:Power of Element/Magma with Identity
- Definition:Power of Element/Notation
- Definition:Power of Element/Notation/Semigroup
- Definition:Power of Element/Semigroup