(algebra, ring theory) Given an integral domain R and its field of fractions K = Frac(R), an R-submodule I of K such that for some nonzero r∈R, rI ⊆ R.

(algebra, ring theory) For given ring R, any ideal I such that Q = R / I, the set of cosets of elements of I in R, is a ring (the quotient ring of I in R).

(algebraic geometry) An ideal consisting of all polynomials (belonging to a certain polynomial ring) which zero out within a given algebraic variety.

ideally; if only it were possible.

plural of ideal triangle

Nonstandard spelling of beau idéal.

Alternative form of beau idéal

In hyperbolic geometry, a triangle whose vertices are all ideal; i.e. points at infinity, rather than real.

(physics) a hypothetical gas, whose molecules exhibit no interaction, and undergo elastic collision with each other and with the walls of the container

plural of ideal gas