Primitive ideal

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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.


[1] N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956)
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Primitive ideal. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by K.A. Zhevlakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article