# Category:Products

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This category contains results about Products in the context of Algebra.

Definitions specific to this category can be found in Definitions/Products.

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

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

### Definition by Index

The composite is called the **product** of $\tuple {a_1, a_2, \ldots, a_n}$, and is written:

- $\displaystyle \prod_{j \mathop = 1}^n a_j = \paren {a_1 \times a_2 \times \cdots \times a_n}$

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Products"

The following 17 pages are in this category, out of 17 total.

### P

### S

- Sum of Elements in Inverse of Cauchy Matrix
- Summation by k of Product by r of x plus k minus r over Product by r less k of k minus r
- Summation by k of Product by r of x plus k minus r over Product by r less k of k minus r/Example
- Summation of General Logarithms
- Summation of Powers over Product of Differences
- Summation of Powers over Product of Differences/Example