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.
|||N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956)|
Primitive ideal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Primitive_ideal&oldid=16446