Re: [代數] 群、環、體的由來?

[hips (hips)]

http://math.berkeley.edu/~gbergman/

You ask about the mathematical use of words like "field" and "ring"
(p.1).

I think that "field", "ring", "group" and "domain" are all cases where
mathematicians chose a general word meaning "a collection of things
that one can choose from", and gave it a technical meaning.  I don't
think that any particular differences between the meanings of those
words motivated these choices; whoever came first got first pick.

So far as I know, all European languages use for "ring", "group" and
"(integral) domain" words having the same literal meanings as the
English ones; but for "field" they are split:  English and Spanish
use the word meaning a (farmer's) field, while French and German use
the word for "body" (French "corps", German "Koerper").  For the
analogous structures but where multiplication may be noncommutative,
these languages use modified terms:  "skew field", "corps gauche",
"Schiefkoerper".  But Russian avoids this awkwardness:  Someone must
have noticed the situation in Western languages, and cleverly assigned
their word for "field" (polya) to the commutative concept, and the word
for "body" (telo) to the one without an assumption of commutativity.

I have sometimes conjectured that the choice of the word "ring" was
a pun:  A subset of  C  is a ring if and only if it is "closed" under
the appropriate operations.  (On the other hand,  Z/n  can be thought
of as ring-like in a different way.)

---
代數裡面怪怪的名字很多,
比方為什麼ideal要叫做ideal而不是normal subring?
諸如此類.

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 98.154.98.252
→ Sfly        :ideal跟數論有關, 是從"理想數"來的
→ GaussQQ     :ideal這個概念可以去看Kummer 為了解決費馬問題提出
→ GaussQQ     :來的
推 recorriendo :ideal的相關概念都是跟普通subgroup類比而不是normal
→ recorriendo :supgroup 像generator就是