On the ideals of a Noetherian ring
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- by J. T. Stafford PDF
- Trans. Amer. Math. Soc. 289 (1985), 381-392 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- 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