Englisch-Finnisch Übersetzung für direct product

Definition für 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

Anwendungsbeispiele

  • 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 2^n (or dimension n) may be constructed as the direct product of n Boolean rings of dimension one.

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