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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Note on simple integral extension domains and maximal chains of prime ideals


Author: L. J. Ratliff
Journal: Proc. Amer. Math. Soc. 77 (1979), 179-185
MSC: Primary 13B20; Secondary 13A15
DOI: https://doi.org/10.1090/S0002-9939-1979-0542081-X
MathSciNet review: 542081
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Abstract: It is shown that if R is a semi-local (Noetherian) domain, then there exists a simple integral extension domain $ R[e]$ of R such that there exists a maximal chain of prime ideals of length n in some integral extension domain of R if and only if there exists a maximal chain of prime ideals of length n in $ R[e]$. An interesting existence theorem on a certain type of height one prime ideals in $ R[X]$ follows.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0542081-X
Keywords: Integral extension ring, maximal chain of prime ideals, polynomial ring, semi-local ring, simple extension ring, Upper Conjecture
Article copyright: © Copyright 1979 American Mathematical Society

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