Timeline for Why is a ring called a "ring"?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 30, 2012 at 17:20 | comment | added | Tim | @Theo Buehler: Hanging out at MSE paid off! | |
| Dec 28, 2012 at 12:43 | comment | added | user9072 | @Joseph O'Rourke: You are welcome, and thank you for the kind words! | |
| Dec 27, 2012 at 13:44 | comment | added | Joseph O'Rourke | @quid: Thanks for this remarkably erudite answer! I especially like your explanation "why a ring is a ring even though it is not more ring-like than a group or a field; the later two already had a different name." This makes perfect sense to me. We all create names for our mathematical constructs, and often the best names are already "taken," forcing us to perhaps slightly misname. | |
| Dec 27, 2012 at 13:41 | vote | accept | Joseph O'Rourke | ||
| Dec 27, 2012 at 13:17 | comment | added | user9072 | To mention one very pertinent information from Theo Buehler's answer also directly here: Noether (1921) uses an axiomatization of commutative ring essentially as in use today and as in 'Moderne Algebra' (crediting Fraenkel, but mentioning the modification). The last sentence in my earlier comment was based on a too quick reading: Noether does not directly consider integral domains without unit, but uses and additional adjective, she there calls a comm. ring with unit and without zero-div a 'eigentliche Integritätsbereich' (so something like proper inetegral domains). | |
| Dec 27, 2012 at 12:34 | comment | added | user9072 | @Theo Buehler: Thanks for the interesting pointer, this is interesting! I just was in the process of editing in Fraenkel and Steinitz while you commented, and did not see you comment before finalizing this. Sorry! So, I reproduced a small part of yours; but I think/hope at least Steinitz is a new piece of information. It is interesting that Noether also in 1921 does not impose unit for intergral domains. | |
| Dec 27, 2012 at 12:22 | history | edited | user9072 | CC BY-SA 3.0 |
expanded (Fraenkel, Steinitz) and slightly changed
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| Dec 27, 2012 at 12:07 | comment | added | Theo Buehler | Hi quid. It seems to me that the sources I give in the answer to where does the term “integral domain” come from? are somewhat relevant to your answer (bridging the gap between Hilbert and Moderne Algebra): math.stackexchange.com/q/45945 The history of the concept of rings (as opposed to the etymology) was also discussed in this thread: math.stackexchange.com/q/362 | |
| Dec 27, 2012 at 10:19 | history | answered | user9072 | CC BY-SA 3.0 |