Primitive ideal

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Not to be confused with primary 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. Note that (despite the name) 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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