WHEN IS THE SET OF INTERMEDIATE RINGS A FINITE BOOLEAN ALGEBRA

Authors : Ahmed Ayache

Pages : 129-139

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Publication Date : 2010-12-01

Article Type : Research Paper

Abstract :Let R ⊂ S be an extension of integral domains with identity such that R is not a field and R is integrally closed in S. We determine necessary and sufficient conditions so that the set of intermediate rings [R, S] between R and S is a finite boolean algebra. Several cases are treated, specially when S is the quotient field of R or when R is a Krull domain.
Keywords : Boolean algebra, normal pair, minimal overring, maximal chain