(algebra, commutative algebra, ring theory) An ideal I within a ring R that is its own radical (i.e., for any r ∈ R, if rⁿ ∈ I for some positive integer n, then r ∈ I).

plural of beau-ideal

Alternative form of beau idéal

(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.

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

plural of ideal triangle

(physics) the equation of state of an ideal gas

(sociology) Behaviour that is characterized by both the desire and the ability to progress towards an ideal by choosing a new goal when a previous one has been met or the effort to meet it has failed.

(algebra) An integral domain in which every ideal is a principal ideal.