A note on Jacobson rings and polynomial rings

Ferrero, Miguel; Parmenter, Michael M.

doi:10.1090/S0002-9939-1989-0929416-7

A note on Jacobson rings and polynomial rings
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by Miguel Ferrero and Michael M. Parmenter PDF

Proc. Amer. Math. Soc. 105 (1989), 281-286 Request permission

Abstract:

As is well known, if $R$ is a ring in which every prime ideal is an intersection of primitive ideals, the same is true of $R[X]$. The purpose of this paper is to give a general theorem which shows that the above result remains true when many other classes of prime ideals are considered in place of primitive ideals.

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