The set of indeterminate rings of a normal pair as a partially ordered set |
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Authors: | Ahmed Ayache |
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Affiliation: | 1.Department of Mathematics, Faculty of Science,University of Sana’a,Sana’a,Yemen |
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Abstract: | Let R ì S{Rsubset S} be an extension of integral domains and let [R, S] be the set of intermediate rings between R and S ordered by inclusion. If (R, S) is normal pair and [R, S] is finite, we do prove that there exists a semi-local Prüfer ring T with quotient field K such that [R,S] @ [T,K]{[R,S]cong lbrack T,K]} (as a partially ordered set). Consequently, any problem relative to the finiteness conditions in [R, S] can be investigated in the particular case where R is a semi-local Prüfer ring with quotient field S. |
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