Comaximizable primes
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- by Raymond C. Heitmann and Stephen McAdam
- Proc. Amer. Math. Soc. 112 (1991), 661-669
- DOI: https://doi.org/10.1090/S0002-9939-1991-1049136-X
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Abstract:
Let ${P_1}, \ldots ,{P_n}\left ( {n \geq 2} \right )$ be not necessarily distinct nonzero prime ideals in the Noetherian, but not Henselian, domain $R$. We show that there is a finitely generated integral extension domain $T$ of $R$, containing distinct, pairwise comaximal prime ideals ${Q_1}, \ldots ,{Q_n}$ lying over ${P_1}, \ldots ,{P_n}$ respectively.References
- C. Chevalley, La notion d’anneau de décomposition, Nagoya Math. J. 7 (1954), 21–33 (French). MR 67866
- William Heinzer and Sylvia Wiegand, Prime ideals in two-dimensional polynomial rings, Proc. Amer. Math. Soc. 107 (1989), no. 3, 577–586. MR 982402, DOI 10.1090/S0002-9939-1989-0982402-3
- Irving Kaplansky, Commutative rings, Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
Bibliographic Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 661-669
- MSC: Primary 13B22; Secondary 13A15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1049136-X
- MathSciNet review: 1049136