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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Rings with annihilator chain conditions and right distributive rings


Authors: Miguel Ferrero and Günter Törner
Journal: Proc. Amer. Math. Soc. 119 (1993), 401-405
MSC: Primary 16P60; Secondary 16D30
MathSciNet review: 1150649
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Abstract: We prove that if a right distributive ring $ R$, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of $ R$ is the right singular ideal of $ R$ and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1150649-2
PII: S 0002-9939(1993)1150649-2
Article copyright: © Copyright 1993 American Mathematical Society