how did groups, rings, fields, ideals, intergal domains etc got their name? It seems a bit uneasy for me if the name of these concepts doesnt make sense. For example the name "vector space" makes sense because it is literally "space filled with vectors". So what is going on with these weird names in abstract algebra ?

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mathmale · Answer

Why not Google "rings:  origin of the term" or something like that?  Bet there's a lot of info on the 'Net just begging to be discovered.

caozeyuan · Answer

@HolsterEmission can you help me alittle on this one. I did google it up, but it is not that helpful since most answers foucus on the "what" rather than "why".

holsteremission · Answer

I'm quite interested myself behind the etymology of each term. I've always wondered if there's a geometric interpretation behind the names, especially for structures like rings and lattices. I know I have a book on group theory lying around somewhere, maybe there's some info I can find there...

caozeyuan · Answer

yea, why a ring, not a disk, a sphere, or a donut? To me the physical ring and the mathematical ring seems rather disconnected, how would a mathematician say they are similiar?

mathmale · Answer

Certainly appreciate your curiosity, tho' there's not much I can do to satisfy it using my current knowledge.  Have you tried googling something like "origin of terminology groups, rings" and see what responses you get.

welshfella · Answer

names may differ from country to country also 
for example in the US  
 sqrt 3 is called a 'radical' while in the UK it is known as a 'surd'.

holsteremission · Answer

So my text (Charles Pinter's "A Book of Abstract Algebra", 2nd ed) doesn't have any details on etymology. A web search pulled up some results, but they don't seem particularly illuminating: http://mathoverflow.net/questions/35286/origins-of-names-of-algebraic-structures The answers posted there don't really address the "why" but rather provide some historical context along with the actual origins of the words themselves (e.g. "ring" is derived from German "Zahlring"). http://mathoverflow.net/questions/117292/why-is-a-ring-called-a-ring The top answer here provides some speculative commentary as to the meaning behind "ring", though in my opinion ultimately doesn't impart any more information about what a ring looks like compared to a group or integral domain. http://math.stackexchange.com/questions/61497/why-are-rings-called-rings The answer here basically suggests that rings and (I'm extrapolating here) all the other structures were named not for any particular intuitive reason, but arbitrarily chosen by the authors. Not a very satisfying result, but sometimes that's what it comes down to...

jdoe0001 · Answer

there isn't .... a consortium of fat guys and gals sitting around a smoke-filled room eating hamburgers and revising profusely the names or making them per se bear in mind that, math notation is just a way to represent phenomena so, the authors, whoever it happens to be, will name it with some mnemonic name hmm a good example of etymologies of that kind would be, say for IT(information technology) two guys from I think it was IBM, used to go with their laptop to a mexican restaurant and they were working on a bootcode and bootloader for optical media at the time, only "fixed" media had usable bootloaders so, they succeeded, a way to make CDs be bootable, you stick in the tray and off it boots up but they had no name for it in the end, they named it, the restaurant's name https://en.wikipedia.org/wiki/El_Torito_(CD-ROM_standard)

caozeyuan · Answer

This is exactly what I got on google, so I still dont know does the name ring comes out because it has some similiarity to the ring in our normal world