Domain (Ring theory)

Revision as of 16:29, 5 September 2008 by Jam (talk | contribs) (New page: A ring, <math>R</math>, is an '''domain''' if: * <math>0\neq 1</math> (where <math>0</math> and <math>1</math> are the additive and multiplicative identities, respectively) * and it c...)
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A ring, $R$, is an domain if:

  • $0\neq 1$ (where $0$ and $1$ are the additive and multiplicative identities, respectively)
  • and it contains no zero divisors (i.e. there are no nonzero $x,y\in R$ such that $xy = 0$).

If $R$ is also commutative, than it is an integral domain.

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