In the physics lab, ideal gases are often used to test thermodynamic theories.

In lattice theory, a Frink ideal is a special kind of subset of a partially ordered set that is closed under directed joins.

In commutative algebra, a radical ideal is an ideal I such that whenever a power r^n of an element r in the ring belongs to I for some positive integer n, then r itself belongs to I.

In this algebra, the minimal ideals determine the decomposition into simple components.

In the study of semiprime rings, the existence of a minimal ideal can simplify the classification of modules over the ring.

In many algebraic structures, maximal ideals determine the local behavior of rings.

She carefully examined the radical ideals that inspired the movement, searching for any contradictions.

We used an ideal-typical model to compare different forms of bureaucracy in our study.

Many characters in the novel chase a fleeting beau ideal that never quite materializes.

To determine the geometry of the curve, we computed its vanishing ideal in the polynomial ring and examined its generators.