Definition:Power Structure

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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.