# Primitive ideal

From Encyclopedia of Mathematics

*right primitive ideal*

A two-sided ideal of an associative ring (cf. Associative rings and algebras) such that the quotient ring is a (right) primitive ring. Analogously, by using left primitive rings one can define left primitive ideals. The set of all primitive ideals of a ring, endowed with some topology, is useful in the study of various classes of rings. Usually is topologized using the following closure relation:

where is a subset in . The set of all primitive ideals of a ring endowed with this topology is called the structure space of this ring.

#### References

[1] | N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956) |

**How to Cite This Entry:**

Primitive ideal.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Primitive_ideal&oldid=16446

This article was adapted from an original article by K.A. Zhevlakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article