Name given to an algebraic structure(A, ⊕ , ⊗) that consists of a set A in which two operations ⊕ and ⊗ are internal composition laws that satisfy the following axioms :

  1. (A, ⊕) forms a commutative group;
  2. The operation ⊗, defined by A, is associative and distributes over the operation ⊕.

  • Commutative ring
    Ring in which the second composition law ⊗ is also commutative.
  • Ordered ring
    Ring in which a total order compatible with the law of composition ⊕ can be defined.


The set \(\mathbb{Z}\) with operations + and × is a ring whose neutral elements are 0 and 1, respectively.

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