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On $ K$-primitive rings


Author: Thomas P. Kezlan
Journal: Proc. Amer. Math. Soc. 74 (1979), 24-28
MSC: Primary 16A20
DOI: https://doi.org/10.1090/S0002-9939-1979-0521867-1
MathSciNet review: 521867
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Abstract: Ortiz has defined a new radical for rings, called the K-radical, which in general lies strictly between the prime radical and the Jacobson radical. In this paper a simple internal characterization of K-primitive rings is given, and it is shown that among the K-primitive rings are prime Noetherian rings and prime rings which satisfy a polynomial identity. In addition an analogue of the density theorem is proved for K-primitive rings.


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

  • [1] A. H. Ortiz, On the structure of semiprime rings, Proc. Amer. Math. Soc. 38 (1973), 22-26. MR 47 #1847. MR 0313292 (47:1847)
  • [2] E. C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), 180-183. MR 22 #2626. MR 0111765 (22:2626)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0521867-1
Keywords: K-primitive ring, Noetherian ring, PI-ring, Ore domain, injective hull, quasi-injective hull, density theorem
Article copyright: © Copyright 1979 American Mathematical Society

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