(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.

(algebra, ring theory) A ring that contains no nontrivial ideals (i.e., no (two-sided) ideals other than the zero ideal and the ring itself).

A toroidal vortex in a fluid or gas, i.e. a region where the fluid mostly spins around an imaginary axis line that forms a closed loop.

(historical) A Victorian love token, a ring set with precious stones whose initial letters spelled regard (e.g. ruby, emerald, garnet, amethyst, ruby, diamond) or some other word of affection.

Having the shape of a ring; circular; annular.

plural of ring singularity Synonym of ringularities

Synonym of ringularity

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

(algebra) An integral domain D such that for every element x of its field of fractions F, at least one of x or x⁻¹ belongs to D.

(geometry, dated) A torus.