(algebra, ring theory) A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.

(nautical) A ring of metal attached to a dock to which boats may be attached by a rope.

A signet ring bearing an image of Saint Peter fishing, used in signing papal briefs.

Third-person singular simple present indicative form of ring around

present participle of ring around

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.

plural of thumb-ring

A ring fastened to the guard of a dagger or sword to protect the wielder's hand.

plural of polynomial ring