In commutative algebra, prime ideals correspond to irreducible closed subsets of the spectrum.

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

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

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

Algebraists often classify left ideals by their generators to understand module structure.