A ring is left Noetherian when every ascending chain of left ideals stabilizes, equivalently when every left ideal is finitely generated.
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- Ascending filtered-graded transfer of Noetherianity
- Finite minimal primes and nilpotent prime radical
- Group rings of poly-(cyclic or finite) groups are Noetherian
- Left Noetherian domain Ore lemma
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 2 / 1 / iii / Solution
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 2 / 1 / i / Solution
- Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 2 / 4 / ii / Solution
- Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 1 / 3 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 2 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 2 / 6 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 6 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 6 / 6 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 8 / 1 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 8 / 2 / Solution
- Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 139 / 1 / a / Solution
- Past exam of the non-commutative rings course of the University of Oxford / 2023 / 2 / a / ii / Solution
- Skew Hilbert basis theorem
- Skew polynomial ring of an automorphism
- Top Ext detects finite projective dimension over a left Noetherian ring
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