Artinian ring
= Artinian ring
{wiki=Artinian_ring}
An Artinian ring is a type of ring in ring theory, which is a branch of abstract algebra. A ring \\( R \\) is called Artinian if it satisfies the descending chain condition (DCC) on ideals. This means that any descending chain of ideals in \\( R \\): \\\[ I_1 \\supseteq I_2 \\supseteq I_3 \\supseteq \\ldots \\\] eventually stabilizes, i.e.