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A note on Jacobson rings and polynomial rings


Authors: Miguel Ferrero and Michael M. Parmenter
Journal: Proc. Amer. Math. Soc. 105 (1989), 281-286
MSC: Primary 16A21
DOI: https://doi.org/10.1090/S0002-9939-1989-0929416-7
MathSciNet review: 929416
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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.


References [Enhancements On Off] (What's this?)

  • [1] S. A. Amitsur, Radicals of polynomial rings, Canad. J. Math. 8 (1956), 355-361. MR 0078345 (17:1179c)
  • [2] A. D. Bell, When are all prime ideals in an Ore extension Goldiet?, Comm. Algebra 13 (1985), 1743-62. MR 792560 (86j:16003)
  • [3] M. Ferrero, Prime ideals in polynomial rings, preprint.
  • [4] K. R. Goodearl, Ring theory, nonsingular rings and modules, Marcel Dekker, New York, 1976. MR 0429962 (55:2970)
  • [5] I. N. Herstein, Rings with involutions, Univ. of Chicago Press, Chicago and London, 1976. MR 0442017 (56:406)
  • [6] K. R. Pearson, W. Stephenson and J. F. Watters, Skew polynomials and Jacobson rings, Proc. London Math. Soc. 42 (1981), 559-576. MR 614734 (82j:16058)
  • [7] J. F. Watters, Polynomial extensions of Jacobson rings, J. Algebra 36 (1975), 302-308. MR 0376765 (51:12940)
  • [8] -, The Brown-McCoy radical and Jacobson rings, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 24 (1976), 91-99. MR 0409539 (53:13293)

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DOI: https://doi.org/10.1090/S0002-9939-1989-0929416-7
Article copyright: © Copyright 1989 American Mathematical Society

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