Domain (Ring theory)

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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