Definition:Product Notation (Algebra)/Index

Definition
Let $\left({S, \times}\right)$ be an algebraic structure where the operation $\times$ is an operation derived from, or arising from, the multiplication operation on the natural numbers.

Let $\left({a_1, a_2, \ldots, a_n}\right) \in S^n$ be an ordered $n$-tuple in $S$.

The composite is called the product of $\left({a_1, a_2, \ldots, a_n}\right)$, and is written:


 * $\displaystyle \prod_{j \mathop = 1}^n a_j = \left({a_1 \times a_2 \times \cdots \times a_n}\right)$