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subfield [2013/09/05 20:39] nikolaj |
subfield [2014/03/21 11:11] (current) |
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| ===== Subfield ===== | ===== Subfield ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $\langle F,+,*\rangle \in \mathrm{field}(F) $ | | + | | @#55CCEE: context | @#55CCEE: $\langle F,+,*\rangle \in \mathrm{field}(F) $ | |
| - | | @#FFBB00: $\langle F',+',*'\rangle\in\mathrm{subfield}(\langle F,+,*\rangle) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $\langle \hat F,\hat +,\hat*\rangle\in\mathrm{subfield}(\langle F,+,*\rangle) $ | |
| - | | @#55EE55: $ 0,1\in F' $ | | + | | @#55EE55: postulate | @#55EE55: $ 0,1\in \hat F $ | |
| - | | $x,y\in F'$ | | + | | $x,y\in \hat F$ | |
| - | | @#55EE55: $ x+y,\ x*y,\ x-y,\ x*y^{-1},\ x+'y,\ x*'y,\ x-'y,\ x*y^{-1'} \in F' $ | | + | | @#55EE55: postulate | @#55EE55: $ x+y,\ x*y,\ x-y,\ x*y^{-1}\in \hat F $ | |
| + | | @#55EE55: postulate | @#55EE55: $ x\ \hat +\ y,\ x\ \hat *\ y,\ x\ \hat -\ y,\ x*y^{\hat{-1}} \in \hat F $ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Field_%28mathematics%29|Field]] | Wikipedia: [[http://en.wikipedia.org/wiki/Field_%28mathematics%29|Field]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| - | === Requirements === | + | === Context === |
| [[Field]] | [[Field]] | ||
