Definition:Power (B-Algebra)
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This page is about Power in the context of B-Algebra. For other uses, see Power.
Definition
Let $\struct {X, \circ}$ be a $B$-algebra.
For any $x \in X$ and $n \in \N$, define the $n$th power of $x$, denoted $x^n$, inductively:
- $x^n = \begin{cases}
0 & \text {if $n = 0$} \\ x^{n - 1} \circ \paren {0 \circ x} & \text {if $n \ge 1$} \end{cases}$
Also see
- First Power of Element in $B$-Algebra, demonstrating $x^1 = x$
Sources
- 2002: J. Neggers and Hee Sik Kim: On B-Algebras (Matematički Vesnik Vol. 54: pp. 21 – 29)