When you localize a ring at a prime ideal, many otherwise global obstructions disappear and local properties become easier to study.

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.

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

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

In algebraic number theory, a fractional ideal is an R-submodule of the field of fractions that becomes an ideal of R after multiplication by a suitable nonzero element of R.

Given a ring R and a factor ideal I, the factor ring Q is isomorphic to R/I.

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

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

In an ideal world, everyone would have access to quality education.

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