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I'm curious as to how groups, rings, fields got their names. Did someone just start calling these structures by those names, or is there a (not entirely) arbitrary reason for them?

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    See [this question](http://math.stackexchange.com/q/61497/264) and [this question](http://math.stackexchange.com/q/71129/264) on math.SE, and [this question](http://mathoverflow.net/questions/35286/origins-of-names-of-algebraic-structures) on MathOverflow (and [this question](http://math.stackexchange.com/q/105668/264) and [this question](http://math.stackexchange.com/q/156952/264) for other terminology).2012-07-02
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    See http://en.wikipedia.org/wiki/Group_(mathematics)#History2012-07-02
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    I think Galois used the word _group_ to refer to permutation groups of zeros of polynomials. I think Arthur Cayley is the author of the modern definition, but he was probably just using established terminology rather than endorsing the idea that that's the best possible word.2012-07-02

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