Two notes on imbedded prime divisors
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- by L. J. Ratliff PDF
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Abstract:
The first note shows that if $R < T$ are any two Noetherian rings, then there exists a Noetherian ring $B$ between $R$ and $T$ which has a maximal ideal $N$ such that ${\text {grade}}(N) \leq 1$ and $N \cap R$ is a maximal ideal. The second note shows that if $R$ is a Noetherian ring, then there exists a free quadratic integral extension ring $B$ of $R$ such that $\operatorname {Spec}(B) \cong \operatorname {Spec}(R)$ and such that if $I$ is any regular ideal in $R$ and ${P_1} \cap \cdots \cap {P_g}$ are prime ideals in $R$ containing $I$, then there exists an ideal $J$ in $B$ integrally dependent on $IB$ such that the prime ideals corresponding to the ${P_i}$ are prime divisors of ${J^n}$ for all $n \geq 1$.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 395-402
- MSC: Primary 13A17; Secondary 13E05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908637-1
- MathSciNet review: 908637