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I have always wondered why are the following concepts/objects in Mathematics named so :

1.) Group

2.) Ring

3.) Exterior derivative (in differential geometry)

4.) Interior multiplication (in differential geometry).

5.) 'Soft' & 'Fine' sheaves

Some of these words (like the first two) have a common English usage and I can't see a relation between the common usage and the Mathematical usage so I assume that perhaps there is no connection but am not sure. And I do not understand what is exterior about exterior derivative or what is interior about interior multiplication in differential geometry. Any information about the history of this nomenclature will be helpful. Please feel free to add more words/terms to this list which raise a similar question.

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You might be interested in this website: jeff560.tripod.com/mathword.html –  Najib Idrissi Nov 9 '13 at 14:11
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Algebraic structures are named more or less arbitrarily. They have to be called something, and there's nothing about them that suggests a particular english word, so you just pick something memorable and straightforward. It's just down to what mood the particular mathematician was in on the day they wrote whatever paper contained the first definition. In fact, they're sometimes called completely different things in different languages. The French word for "field" is "body". –  Jack M Nov 9 '13 at 14:13
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