Last Updated
：2025/12/04
ordered ring
Noun
Japanese Meaning
順序環：部分順序が定義された環（代数系）であり、任意の a, b, c ∈ R に対して、a ≤ b なら a + c ≤ b + c が成立し、さらに 0 ≤ c のとき c·a ≤ c·b および a·c ≤ b·c も成立する性質を持つ。
Sense（1）
（ plural ）
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(algebra, order theory, ring theory) 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.
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ordered ring
The ordered ring of continuous real-valued functions on a compact space provides a natural setting for comparing positivity and order-preserving operations.
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The ordered ring of continuous real-valued functions on a compact space provides a natural setting for comparing positivity and order-preserving operations.
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