On finiteness of chains of intermediate rings |
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Authors: | Mabrouk Ben Nasr |
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Affiliation: | (1) Department of Mathematics, Faculty of Sciences of Sfax, BP 802, 3018 Sfax, Tunisia |
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Abstract: | An extension of integral domains 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 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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Keywords: | Ring extension Intermediate chains of domains Normal pair Valuation domain |
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