Prime Ring

Examples

• Any domain.
• Any primitive ring.
• A matrix ring over an integral domain. In particular, the ring of 2-by-2 integer matrices is a prime ring.

Properties

• A commutative ring is a prime ring if and only if it is an integral domain.
• The ring of matrices over a prime ring is a prime ring.
• A ring is prime if and only if its zero ideal is a prime ideal.

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