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.