Talk:Torsion (algebra)
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Etymology and history
[edit]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)
- That's an interesting question, and beause you asked it, I found this resource. Torsion (as used in this sense) is the second torsion entry, and it's pretty informative! If you think this source is sufficiently reliable, we could adapt it for this article... Rschwieb (talk) 18:21, 1 February 2013 (UTC)
- Very interesting. Thanks alot for finding this. The page claims that the entry in question was contributed by a Peter Flor, and that would probably be the Austrian professor emeritus of Mathematics at the University of Graz.[1] So the source is probably reliable. But there appears to be no single, canonical source for the terms in question, and I would hesitate to add speculative content to the article. After all, the front page of Earliest Known Uses of Some of the Words of Mathematics has this to say: “These pages attempt to show the first uses of various words used in mathematics. Research for these pages is ongoing, and a citation should not be assumed to be the earliest use unless it is indicated as such.”[2] — Tobias Bergemann (talk) 10:48, 3 February 2013 (UTC)
"annihilated by any regular element" --> "annihilated by a regular element"
[edit]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)
Definition - non-zero-divsor or just non-zero?
[edit]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.