Abstract
An extension of integral domains \({R\subseteq S}\) is said to have the “finite length of intermediate chains of domains” property (for short FICP) if each chain of intermediate rings between R and S is finite. The main purpose of this paper is to characterize when \({R\subseteq S}\) has FICP in case R * (the integral closure of R in S) is a finite dimensional semilocal domain. This generalizes a theorem due to Gilmer, in which S is the quotient field of R. Examples illustrating the sharpness and the limits of our results are settled.
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Communicated by D. Segal.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nasr, M.B. On finiteness of chains of intermediate rings. Monatsh Math 158, 97–102 (2009). https://doi.org/10.1007/s00605-008-0090-y
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DOI: https://doi.org/10.1007/s00605-008-0090-y