Algebraists often compare ideal numbers across different rings to understand factorization properties.

Every maximal ideal in a commutative ring corresponds to a field when we take the quotient by that ideal.

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

In algebraic number theory, each invertible ideal can be represented by an ideal number in the ring of integers of a number field.

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

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.

For him, the marble statue represented the beau-ideal of classical beauty.

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

In the Poincaré disk model, an ideal triangle has all three vertices on the boundary at infinity.

In hyperbolic geometry, ideal triangles serve as the basic building blocks for understanding tessellations of the plane.