Abnormalities in Noetherian rings
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- by J. T. Arnold and M. B. Boisen PDF
- Proc. Amer. Math. Soc. 73 (1979), 1-6 Request permission
Abstract:
If $P \subseteq Q$ are prime ideals in some ring R and if rank $Q = {\text {rank}}(Q/P) + {\text {rank}}\;P + k$, then $P \subset Q$ is said to be k-abnormal and k is called the degree of abnormality. The paper consists of two examples. The first example is a Noetherian integral domain in which the set of degrees of abnormality is unbounded. Let P be a prime ideal of R and set $W = \{ Q/Q$ is a prime ideal and $P \subset Q$ is abnormal}. The second example is a local domain such that $\{ k|P \subset Q$ is k-abnormal for some $Q \in W\} \ne \{ k|P \subset Q$ is k-abnormal for some Q minimal in W}.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 1-6
- MSC: Primary 13E05; Secondary 13C15
- DOI: https://doi.org/10.1090/S0002-9939-1979-0512046-2
- MathSciNet review: 512046