Factor ideals often reveal hidden structure in algebraic number fields.

Fractional ideals often determine the class group of a Dedekind domain, revealing essential arithmetic information.

In the primary decomposition of an ideal, primary ideals capture the multiplicity and embedded components.

The artist's portraits tried to capture various beau-ideals rather than a single perfect type.

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

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.

In his paper, he showed that Frink ideals behave well under directed limits.

In the seminar, the mathematician illustrated how right ideals behave differently from left ideals in noncommutative rings.

In the ring of integers, principal ideals play a central role in understanding factorization.