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Can somebody add something to the article about the etyomology and the history of the terms torsion module, torsion group etc.? As in, who defined these terms first, and when? And why did he or she use the term "torsion"? — Tobias Bergemann ( talk) 09:32, 1 February 2013 (UTC)
This is found at the very beginning of the article.
The word "any", according to this StackExchange/Mathematics question, is ambiguous in general. Here, it sounded like "every" to my ears. I think "any" does mean "every" in this context.
--— manual signature: comment added by ThoAppelsin ( talk • contribs) 10:39, 24 December 2019 (UTC)
The current article has the definition:
"In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring."
By that definition, a ring R considered as a module M over itself has only zero as its torsion element. Is that the intent of the definition?
For m in M (and thus in R) and r in R, suppose that m*r = 0. Unless m = 0, we have that r is a zero divisor.
Tashiro~enwiki ( talk) 20:57, 31 July 2023 (UTC)