division ring

(idea) by Noether Wed Jul 12 2000 at 6:13:06
R is a division ring if
  • R is a ring
  • For each nonzero element a in R there exists an inverse a-1 in R with aa-1=a-1a=1

    A commutative division ring is a field. An example of a noncommutative division ring is H Hamilton's ring of Quaternions.

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