English-Danish translations for direct product
Definition of direct product
- The set of all possible tuples whose elements are elements of given, separately specified, sets
- Such a set of tuples formed from two or more groups, forming another group whose group operation is the component-wise application of the original group operations and of which the original groups are normal subgroups
- Such a set of tuples formed from two or more rings, forming another ring whose operations arise from the component-wise application of the corresponding original ring operations
- A topological space analogously formed from two or more topological spaces
- A high-level generalization of the preceding that applies to objects in an arbitrary category and produces a new object constructable by morphisms from each of the original objects
Examples
- If A and B are sets, their direct product is the set of ordered pairs (a,b) with a in A and b in B
- A Boolean ring of order (or dimension ) may be constructed as the direct product of Boolean rings of dimension one.
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