Artinian ideal

In algebra, specifically in the theory of rings and modules, an *Artinian ideal* typically refers to an ideal in a ring that satisfies the descending chain condition (DCC). This means that any descending chain of ideals within an Artinian ideal eventually stabilizes; that is, there are no infinite descending sequences. More generally, a ring is called an *Artinian ring* if it satisfies the descending chain condition for ideals.