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A Note on Jacobson Rings and Polynomial Rings

1989
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Proceedings of the American Mathematical Society
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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 rnany other classes of prime ideals are considered in place of prirnitive ideals. Throughout this paper we assume that R is a ring with identity element and R[X] is the polynomial ring over R in an indeterminate X . A ring R is said to be a Jacobson ring if

doi:10.2307/2046937
fatcat:wzmwfpv6kjaytgb4erpj2n6w3q