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# prime ring

A ring $R$ is said to be a *prime ring* if the zero ideal is a prime ideal.

If a prime ring $R$ is commutative, then it is a cancellation ring. If in addition $R$ has a multiplicative identity $1\neq 0$, then it is an integral domain.

Related:

ZeroIdeal

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

16U99*no label found*16N60

*no label found*

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