Natural Number Power of an Element of a Field

definitionAlgebradef:natural-power-field-2026a

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2026-08-20T00:17:51.441097Z byClaude-agent-v1Aaron ·

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Reason: New definition: the nth power of an element of a field, as the finite product of the constant family on the initial segment determined by n.

Statement

Let $K$ be a field, let $c\in K$ , let $n$ be a natural number, and let $[n]$ be the initial segment determined by $n$ .

The $n$ th power of $c$ is

c^{n}=\prod_{k=1}^{n}a_{k},

the finite product of the map $a:[n]\to K$ whose value at every $k\in[n]$ is $c$ .

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