# Differences

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 division_ring [2013/08/05 23:58]nikolaj division_ring [2017/03/25 15:59]nikolaj Both sides previous revision Previous revision 2017/03/25 15:59 nikolaj 2014/03/21 11:11 external edit2013/08/05 23:58 nikolaj 2013/08/05 23:56 nikolaj 2013/08/05 23:53 nikolaj 2013/08/05 23:52 nikolaj created Next revision Previous revision 2017/03/25 15:59 nikolaj 2014/03/21 11:11 external edit2013/08/05 23:58 nikolaj 2013/08/05 23:56 nikolaj 2013/08/05 23:53 nikolaj 2013/08/05 23:52 nikolaj created Line 1: Line 1: ===== Division ring ===== ===== Division ring ===== - ==== Definition ​==== + ==== Set ==== - | @#88DDEE: $X$ | + | @#55CCEE: context ​    | @#55CCEE: $X$ | - + | @#55EE55: postulate ​  | @#55EE55: $\langle X,+,* \rangle \in \mathrm{divisionRing}(X)$ | - | @#55EE55: $\langle X,+,* \rangle \in \mathrm{divisionRing}(X)$ | + | @#55CCEE: context ​    | @#55CCEE: $\langle X,+,* \rangle \in \mathrm{unitalRing}(X)$ | - + | @#55CCEE: context ​    | @#55CCEE: $\langle X,* \rangle \in \mathrm{group}(X)$ | - | @#88DDEE: $\langle X,+,* \rangle \in \mathrm{unitalRing}(X)$ | + | @#DDDDDD: range       | @#DDDDDD: $a,b\in X$ | - | @#88DDEE: $\langle X,* \rangle \in \mathrm{group}(X)$ | + | @#55EE55: postulate ​  | @#55EE55: $\exists a,b.\ (a\neq b)$ | - + - | @#DDDDDD: $a,b\in X$ | + - + - | @#55EE55: $\exists a,b.\ (a\neq b)$ | + ==== Ramifications ==== ==== Ramifications ==== Line 19: Line 15: ==== Reference ==== ==== Reference ==== Wikipedia: [[http://​en.wikipedia.org/​wiki/​Division_ring|Division ring]], [[http://​en.wikipedia.org/​wiki/​Trivial_ring|Trivial ring]] Wikipedia: [[http://​en.wikipedia.org/​wiki/​Division_ring|Division ring]], [[http://​en.wikipedia.org/​wiki/​Trivial_ring|Trivial ring]] - ==== Context ​==== + ==== Parents ​==== === Subset of === === Subset of === [[Unital ring]] [[Unital ring]]