On 
-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 | References | Similar Articles | Additional Information
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.
- [1] Augusto H. Ortiz, On the structure of semiprime rings, Proc. Amer. Math. Soc. 38 (1973), 22–26. MR 0313292, https://doi.org/10.1090/S0002-9939-1973-0313292-8
- [2] Edward C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), 180–183. MR 0111765, https://doi.org/10.1090/S0002-9939-1960-0111765-5
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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
