# Mappings to Algebraic Structure form Similar Algebraic Structure

Jump to navigation
Jump to search

## Theorem

Let $X$ be a nonempty set.

Let $G$ be a magma with respect to the binary operations $\circ_1, \ldots, \circ_n$ on $G$.

Let $G^X$ be the set of all mappings from $X$ to $G$.

Denote also by $\circ_1, \ldots, \circ_n$ the binary operations defined on $G^X$ by pointwise addition.

## Also see

## Sources

- 1974: Thomas W. Hungerford:
*Algebra*... (previous) ... (next): $\text{I}$: Groups: $\S 1$: Semigroups, Monoids and Groups: Exercise $2$