Attribution and licences
Original course writing: GPT-6.1 Sol (OpenAI), Codex, Ultra, October 2026. The original authorship, source credits, copyright notices and adaptation History remain in each complete lesson.
AI Integrated Stacks Project: the credited edition of the Stacks Project and its identified editorial companions. Incorporated Stacks material retains Copyright (C) 2005–2025 Johan de Jong and GNU Free Documentation License 1.2 or later, without Invariant Sections or cover texts. The licence of each combined lesson is listed below.
Complete GNU FDL 1.2. Original components retain their CC0 dedication. Referenced works retain their own terms. Reader and navigation adaptation: OpenAI Codex, GPT-6 Astra, Ultra, 3 October 2026. MathJax retains its bundled notices.
- Spectra of rings: CC0-1.0
- Localization, local properties and support: CC0-1.0
- Noetherian and Artinian rings: CC0-1.0
- Associated primes and primary decomposition: CC0-1.0
- Integral extensions: lying over, going up and going down: CC0-1.0
- The Nullstellensatz and Jacobson rings: CC0-1.0
- Resolutions, Tor and Ext: CC0-1.0
- Tor and flat modules: GFDL-1.2-or-later
- Faithful flatness and the local criterion for flatness: CC0-1.0
- Krull dimension and Noether normalization: GFDL-1.2-or-later
- Graded modules and Hilbert–Samuel functions: CC0-1.0
- Dimension theory of Noetherian local rings: GFDL-1.2-or-later
- Regular sequences, depth and Cohen–Macaulay modules: GFDL-1.2-or-later
- Projective dimension and the Auslander–Buchsbaum formula: CC0-1.0
- Regular local rings: CC0-1.0
- Discrete valuation rings, normal rings and Serre's criterion: CC0-1.0
- Kähler differentials: GFDL-1.2-or-later
- Formally smooth, unramified and étale ring maps: CC0-1.0
- Smooth algebras over a field and the Jacobian criterion: CC0-1.0
- Completion: CC0-1.0
- Coefficient rings and the Cohen structure theorem: GFDL-1.2-or-later
- Henselian local rings and henselization: GFDL-1.2-or-later