# nLab descending chain condition

## Definition

A ring $R$ is said to satisfy the descending chain condition on left (resp. right, two-sided) ideals if any totally ordered subset $\mathcal{S}$ of the set of left (resp. right, two-sided) ideals of $R$ (in the partial order given by the inclusion) has a minimum.

Revised on February 15, 2016 14:05:33 by Urs Schreiber (31.55.9.40)