- International Electronic Journal of Algebra
- Vol: 8 Issue: 8
- WHEN IS THE SET OF INTERMEDIATE RINGS A FINITE BOOLEAN ALGEBRA
WHEN IS THE SET OF INTERMEDIATE RINGS A FINITE BOOLEAN ALGEBRA
Authors : Ahmed Ayache
Pages : 129-139
View : 16 | Download : 11
Publication Date : 2010-12-01
Article Type : Other
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