I've always been curious as to why most algebraic structures were originally given their names. Specifically, I'm curious as to what motivated the names "ring" and "magma." Does anybody have any insights on this?
I have only partial information based on a quick search in Wikipedia.
According to Wikipedia, Hilbert coined the term "ring" (Zahlring) in an article written in 1897 titled Die Theorie der algebraischen Zahlkörper.
Ring (mathematics) - Wikipedia, the free encyclopedia
Also according to Wikipedia, the term "magma" was coined by Bourbaki.
http://en.wikipedia.org/wiki/Magma_(algebra)
I'm just guessing, but maybe the term "magma" was chosen because an algebraic magma has very little structure, something like a magma flow.
Yeah, I saw both of those wikipedia articles before posting. After searching around, I found this:
Etymology of Algebraic Structures Martin’s Blog
It looks like you were right about the name "magma." Also, it looks like rings derive their name from the cyclic structure of such rings as Z/nZ. Still, that list seems a bit unsure of itself. I'm still open to any information anyone happens to have on this subject.
"Group" seems kinda obvious to me.
Because "group" sounds similar to a "set", as in a collection of objects.
Which is why Galois was motivated to use this term.
We also need to remember that the original definitions for these terms were not as abstract. For example, "ring", in the older days, could have referred to very specific set of algebraic numbers which certain properties. Perhaps, like the cyclic property as mentioned in that website. And thus, the originator of this term was motivated to use "ring". However, in the future mathematicians made the definition more abstract and in the process keeping the old term.
The world "field" in the older days would to refer to a subset of complex numbers satisfies the necessary conditions of being a field. But why "field" was chosen I have no idea.