ordered ring
ordered ring · ordered rings
A ring, R, equipped with a partial order, ≤, such that for arbitrary a, b, c ∈ R, if a…A ring, R, equipped with a partial order, ≤, such that for arbitrary a, b, c ∈ R, if a ≤ b then a + c ≤ b + c, and if, additionally, 0 ≤ c, then both ca ≤ cb and ac ≤ bc.
Meaning
2 sensesA ring, R, equipped with a partial order, ≤, such that for arbitrary a, b, c ∈ R, if a ≤ b then a + c ≤ b + c, and if, additionally, 0 ≤ c, then both ca ≤ cb and ac ≤ bc.
A ring, R, equipped with a total order, ≤, such that for arbitrary a, b, c ∈ R, if a ≤ b then a + c ≤ b + c, and if, additionally, 0 ≤ c, then both ca ≤ cb and ac ≤ bc.
Forms
plural: ordered rings| Singular | ordered ring |
|---|---|
| Plural | ordered rings |
regular
Synonyms
2 synonymsring equipped with a partial order:partially ordered ring
ring equipped with a total order:totally ordered ring
Word family
1 related wordsRelatedordered field