Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

The question was asked by a student, and I did not have a ready answer. I can think of the German word ``Einheit'', but since in German that is not how the identity element of a group is called, I doubt that is the origin. Any ideas?

share|improve this question
5  
"but since in German that is not how the identity element of a group is called" ... Sometimes it is indeed called like this. Also the identity matrix is frequently or at least not rarely called 'Einheitsmatrix'. Another thought: Sometimes the identity element in a multiplicative group is called (perhaps sloppily) Einselement (where 'eins' means 'one'). –  quid Feb 7 '12 at 14:09
add comment

1 Answer 1

up vote 10 down vote accepted

Heinrich Weber uses Einheit and e in his Lehrbuch der Algebra (1896).

share|improve this answer
1  
That is almost certainly the origin, though it should be noted that one in Russian is "edinica". –  Igor Rivin Feb 7 '12 at 14:58
2  
@Igor: The influential early textbooks on algebra tended to be written in German, unfair though that may be to those of us who grew up with English (or Russian). Quite a bit of common terminology and notation in mathematics seems to have originated in German work during the 19th century, such as the symbols $K,k$ for fields. –  Jim Humphreys Feb 7 '12 at 20:55
    
Well, Weber surely popularized the term. But his friend Dedekind used "einheit" before him to mean either a unit in a field, or a unit measure in geometry, and I'll bet if you look in his work you'll find it for groups. Probably if you dig into the 19th century you can find a series of earlier and earlier, vaguer and vaguer, uses of the term for a group identity. –  Colin McLarty Dec 29 '12 at 17:35
1  
In todays German literature, it seems that Einselement (or even neutrales Element) is preferred over Einheit (which is used for units, i.e. invertible elements of a ring). –  Hagen von Eitzen Feb 8 at 21:49
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.