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 $\left({S, \circ_1}\right)$ and $\left({T, \circ_2}\right)$ be algebraic structures.
The (external) direct product $\left({S \times T, \circ}\right)$ of two algebraic structures $\left({S, \circ_1}\right)$ and $\left({T, \circ_2}\right)$ is the set of ordered pairs:
- $\left({S \times T, \circ}\right) = \left\{{\left({s, t}\right): s \in S, t \in T}\right\}$
where the operation $\circ$ is defined as:
- $\left({s_1, t_1}\right) \circ \left({s_2, t_2}\right) = \left({s_1 \circ_1 s_2, t_1 \circ_2 t_2}\right)$
Subcategories
This category has the following 5 subcategories, out of 5 total.
E
F
G
M
Pages in category "Direct Products"
The following 17 pages are in this category, out of 17 total.
E
- Elements of Finite Support form Submagma of Direct Product
- External Direct Product Associativity
- External Direct Product Closure
- External Direct Product Identity
- External Direct Product of Groups is Group
- External Direct Product of Projection with Canonical Injection
- External Direct Product of Semigroups