simple past tense and past participle of order up

(set theory, order theory) That is equipped with a total order, that is a subset of (the ground set of) a partially ordered set whose partial order is a total order with respect to said subset.

plural of ordered ring

(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.

(mathematics) A partially ordered set. / (mathematics) A totally ordered set.

plural of ordered set

(idiomatic) Exactly what is necessary or useful in a given situation; something very beneficial or desirable.

(set theory, order theory, loosely) A set that has a given, elsewhere specified partial order. / (set theory, order theory, formally) The ordered pair comprising a set and its partial order.

(set theory) A set having a specified total order.

plural of totally ordered set