# division ring

A division ring is a ring $D$ with identity such that

• $1\neq 0$

• For all nonzero $a\in D$, there exists $b\in D$ with $a\cdot b=b\cdot a=1$

Every field is a commutative division ring. The Hamiltonian quaternions are an example of a division ring which is not a field.

Title division ring DivisionRing 2013-03-22 11:48:46 2013-03-22 11:48:46 djao (24) djao (24) 10 djao (24) Definition msc 16K99 msc 81P05 skew field