Version history — Commutativity

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Current edition: v2 · 2026-08-30 · prime abstraction

Corrections

Checking this entry found 2 errors, now corrected: against its sources, or where it contradicted itself or its arithmetic did not hold. Each is listed here so a reader can see what changed. How references were checked.

• 2026-06-20 · Citation corrected. Cited Knuth's The Art of Computer Programming (1973) for order-independent reduce operations in MapReduce, which postdates it; the sentence now cites Dean and Ghemawat's MapReduce paper (2004).
• 2026-06-20 · Citation corrected. Cited Bourbaki's volume on set theory for the structure theory of commutative rings; the reference is now Bourbaki's Algèbre commutative (1961–1965).

Editions

Version	Date	Change	What changed
v2	2026-08-30	Removed a trailing section belonging to Associativity, appended by the 2026-04/05 defective write; 4 of this entry's own footnote definitions were kept in place.	prose — detailed body (prose edited)
v1	2026-08-24	First published edition.	first published edition

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