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

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 with a minimal, nonzero ideal , such that is a commutative polynomial ring in variables, and a Noetherian domain 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 in a Noetherian domain such that is not Artinian.

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Additional Information

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