Category:Definitions/Direct Products

This category contains definitions related to Direct Products.
Related results can be found in Category: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:

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