division ring

A division ring is a ring D with identityPlanetmathPlanetmath such that

  • 10

  • For all nonzero aD, there exists bD with ab=ba=1

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

Title division ring
Canonical name DivisionRing
Date of creation 2013-03-22 11:48:46
Last modified on 2013-03-22 11:48:46
Owner djao (24)
Last modified by djao (24)
Numerical id 10
Author djao (24)
Entry type Definition
Classification msc 16K99
Classification msc 81P05
Synonym skew field