User:Fake Proof/Sandbox/Subset Product/Ring

Definition
Let $\struct {R, +, \circ}$ be a ring.

We can define an operation on the power set $\powerset R$ as follows:


 * $\ds \forall A, B \in \powerset R: A \circ_\PP B = \set {\sum_{i \mathop = 1}^n a_i \circ b_i: n \in \N, a_i \in A, b_i \in B}$

This is called the operation induced on $\powerset R$ by $\circ$, and $A \circ_\PP B$ is called the subset product of $A$ and $B$.

It is usual to write $A \circ B$ for $A \circ_\PP B$.

Also see

 * Definition:Product of Fractional Ideals
 * Definition:Product of Ideals of Ring