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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the ideals of a Noetherian ring


Author: J. T. Stafford
Journal: Trans. Amer. Math. Soc. 289 (1985), 381-392
MSC: Primary 16A33; Secondary 16A08, 16A66
DOI: https://doi.org/10.1090/S0002-9947-1985-0779071-5
MathSciNet review: 779071
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Abstract: We construct various examples of Noetherian rings with peculiar ideal structure. For example, there exists a Noetherian domain $ R$ with a minimal, nonzero ideal $ I$, such that $ R/I$ is a commutative polynomial ring in $ n$ variables, and a Noetherian domain $ S$ with a (second layer) clique that is not locally finite. The key step in the construction of these rings is to idealize at a right ideal $ I$ in a Noetherian domain $ T$ such that $ T/I$ is not Artinian.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0779071-5
Keywords: Noetherian rings, ideal structure, idealizers, links between prime ideals and localisation
Article copyright: © Copyright 1985 American Mathematical Society