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Why algebra (over a field) is called "algebra?" (My random guess is that it's a back-formation of some algebras, chopping adjectives from say Lie algebra or Clifford algebra, etc.) And when was that usage established?

Earliest Known Uses of Some of the Words of Mathematics is a fascinating site, but doesn't tell any.

Thanks beforehand.

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I used to think it was because it was a place where you could algebra, in the high-school sense of the word; you can do the usual algebraic operations, solve equations, and so on. But I'm not so sure any more. –  Gerry Myerson Oct 23 '12 at 11:40
    
@GerryMyerson: I have had my own musings about algebraic structures being places in which one can 'do algebra' and certain kinds of equations can be solved. Thinking this way, do you think fields perhaps would be most deserving of the name 'algebra'? –  Alex Petzke Mar 5 '13 at 22:47
    
@Alex, probably. But that train has left the station. –  Gerry Myerson Mar 5 '13 at 23:13
    
@Gerry: True. I just found that I could relate to your thought, and decided I might as well throw that out there. –  Alex Petzke Mar 5 '13 at 23:50

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