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