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division_ring [2013/08/05 23:56]
nikolaj
division_ring [2013/08/05 23:58]
nikolaj
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 ==== Ramifications ==== ==== Ramifications ====
 === Discussion === === Discussion ===
-A division ring is essentially two compatible groups over a set $X$, one of which is necessarily commutative. The second requirement distinguishes the division ring from a unital ring by inverses with respect to the multiplication $*$. The last statement says that $\langle X,+,* \rangle$ must not be the trivial ring.+A division ring is essentially two //compatible// groups over a set $X$, one of which is necessarily commutative. ​Compatible in the sense of the distributive laws of a ring, which is asymmetrical with respect to "​$+$"​ and "​$*$"​. 
 + 
 +The second requirement distinguishes the division ring from a unital ring by inverses with respect to the multiplication $*$. The last statement says that $\langle X,+,* \rangle$ must not be the trivial ring.
 ==== 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]]
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