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.

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

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

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 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.

In the seminar, we compared several transcendental idealisms and debated their implications for metaphysics.