# Category:Direct Products

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This category contains results about **Direct Products**.

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

Let $\struct {S, \circ_1}$ and $\struct {T, \circ_2}$ be algebraic structures.

The **(external) direct product** $\struct {S \times T, \circ}$ of $\struct {S, \circ_1}$ and $\struct {T, \circ_2}$ is the set of ordered pairs:

- $\struct {S \times T, \circ} = \set {\tuple {s, t}: s \in S, t \in T}$

where the operation $\circ$ is defined as:

- $\tuple {s_1, t_1} \circ \tuple {s_2, t_2} = \tuple {s_1 \circ_1 s_2, t_1 \circ_2 t_2}$

## Subcategories

This category has the following 9 subcategories, out of 9 total.

### D

### E

### F

### G

### I

## Pages in category "Direct Products"

The following 9 pages are in this category, out of 9 total.