nLab
descending chain condition

Definition

A ring RR is said to satisfy the descending chain condition on left (resp. right, two-sided) ideals if any totally ordered subset 𝒮\mathcal{S} of the set of left (resp. right, two-sided) ideals of RR (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)