## Left/Right Noetherian and Left/Right Artinian Rings

### Counterexamples in Upper Triangles Matrix Rings

The ring is left Noetherian. However, it is not right Noetherian, left Artinian or right Artinian.

Similarly, the ring is left Artinian and left Noetherian, but not right Artinian or right Noetherian.

The details are worked out here under “CIA: Some Upper Triangular Matrix Rings and Noetherian/Artinian Hypotheses.”

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