# Primitive ideal

Not to be confused with primary ideal or principal ideal.

In mathematics, a left **primitive ideal** in ring theory is the annihilator of a simple left module. A right primitive ideal is defined similarly. Left and right primitive ideals are always two-sided ideals.

The quotient of a ring by a left primitive ideal is a left primitive ring.

## References

- Isaacs, I. Martin (1994),
*Algebra*, Brooks/Cole Publishing Company, ISBN 0-534-19002-2

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