ordered ring
An "ordered ring" combines the structures of a ring and a partially or totally ordered set, ensuring compatibility between ring operations and the ordering.
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Definition
C2Abstract Algebra
(technical, academic)A ring with a partial or total order where addition and multiplication respect the order.
Example
- In an ordered ring, if a ≤ b, then adding the same element to both sides preserves the order.
- Multiplying non-negative elements in an ordered ring results in a non-negative product.
Similar
Terms that have similar or relatively close meanings to "ordered ring":
ordered setorder upback orderin orderopen orderjob orderprime ringstanding orderring offrunning ordershort order