Examples of noncatenary rings
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- by Raymond C. Heitmann PDF
- Trans. Amer. Math. Soc. 247 (1979), 125-136 Request permission
Abstract:
A technique is developed for constructing a new family of noetherian integral domains. To each domain, there naturally corresponds its poset (partially ordered set) of prime ideals. The resulting family of posets has the following property: every finite poset is isomorphic to a saturated subset of some poset in the family. In the process, it is determined when certain power series may be adjoined to noetherian rings without destroying the noetherian property.References
- Nicolas Bourbaki, Elements of mathematics. Commutative algebra, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972. Translated from the French. MR 0360549
- Paul M. Eakin Jr., The converse to a well known theorem on Noetherian rings, Math. Ann. 177 (1968), 278–282. MR 225767, DOI 10.1007/BF01350720
- 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
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 247 (1979), 125-136
- MSC: Primary 13A15; Secondary 13C15, 13E05
- DOI: https://doi.org/10.1090/S0002-9947-1979-0517688-0
- MathSciNet review: 517688