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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0517688-0
PII: S 0002-9947(1979)0517688-0
Keywords: Prime ideal poset, catenary rings
Article copyright: © Copyright 1979 American Mathematical Society