# Definition:Power Structure

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## Definition

Let $\struct {S, \circ}$ be an algebraic structure.

Let $\powerset S$ denote the power set of $S$.

Let $\circ_\PP$ denote the operation induced on $\powerset S$ by $\circ$ as follows:

- $\forall A, B \in \powerset S: A \circ_\PP B = \set {a \circ b: a \in A, b \in B}$

Then the resulting algebraic structure $\struct {\powerset S, \circ_\PP}$ is called the **power structure of $\struct {S, \circ}$**.

## Also known as

Some sources refer to this as the **global structure of $\struct {S, \circ}$**.

## Also see

- Results about
**power structures**can be found here.

## Sources

- J.-E. Pin (https://math.stackexchange.com/users/89374/j-e-pin), Is there a name for the algebraic structure formed from the power set of a structure with the operation induced by that power set?, URL (version: 2022-03-23): https://math.stackexchange.com/q/4410785