Name given to an algebraic structure (K, ⊕ , ⊗) formed by a set K in which two operations denoted by ⊕ and ⊗ are second internal binary operation that satisfy the following conditions:

  1. (K, ⊕) forms a commutative group;
  2. (K*, ⊗) forms a group in which K* is composed of all the elements of K except for the neutral element of (K, ⊕);
  3. The operation ⊗ distributes over the operation ⊕.


  • Commutative field
    Field in which the second internal binary operation ⊗ is also commutative.
  • Ordered field
    Field in which a total order can be defined that is compatible with each of the second internal binary operation ⊕ and ⊗.


The sets \(\mathbb{Q}\) and \(\mathbb{R}\) which include the operations + and × are fields whose neutral elements are 0 and 1, respectively.

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