Rings with annihilator chain conditions and right distributive rings
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- by Miguel Ferrero and Günter Törner PDF
- Proc. Amer. Math. Soc. 119 (1993), 401-405 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 401-405
- MSC: Primary 16P60; Secondary 16D30
- DOI: https://doi.org/10.1090/S0002-9939-1993-1150649-2
- MathSciNet review: 1150649