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 :
- (A, ⊕) forms a commutative group;
- 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.
Example
The set \(\mathbb{Z}\) with operations + and × is a ring whose neutral elements are 0 and 1, respectively.