ordered ring

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|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''.
2. {{lb|en|algebra|order theory|ring theory}} 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''.

Source: Wiktionary · CC BY-SA 4.0 (Wiktionary dump) · cached copy, not a rewrite.