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. --

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