Non-Artinian - Mathematics & Logic - Pure Mathematics Dictionary Definition An algebraic object (ring, module, etc.) is non-Artinian if it fails the descending chain condition (DCC): there exists an infinite strictly decreasing chain I1 ⊃ I2 ⊃ I3 ⊃ ··· of subobjects that does not stabilize.
Non-Artinian - Mathematics & Logic - Pure Mathematics Dictionary Definition An algebraic object (ring, module, etc.) is non-Artinian if it fails the descending chain condition (DCC): there exists an infinite strictly decreasing chain I1 ⊃ I2 ⊃ I3 ⊃ ··· of subobjects that does not stabilize.