Examples of noncatenary rings
Author: Raymond C. Heitmann
Journal: Trans. Amer. Math. Soc. 247 (1979), 125-136
MSC: Primary 13A15; Secondary 13C15, 13E05
MathSciNet review: 517688
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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.
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N. Bourbaki, Commutative Algebra, Hermann, Paris, 1972.
P. Eakin, The converse to a well known theorem on noetherian rings, Math. Ann. 177 (1968), 278-282.
M. Nagata, Local rings, Interscience, New York, 1962.