ON THE MAXIMAL CARDINALITY OF CHAINS OF INTERMEDIATE RINGS

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International Electronic Journal of Algebra
Volume:5 Issue:5
ON THE MAXIMAL CARDINALITY OF CHAINS OF INTERMEDIATE RINGS

ON THE MAXIMAL CARDINALITY OF CHAINS OF INTERMEDIATE RINGS

Authors : David E DOBBS, Gabriel PİCAVET, Martine PİCAVETL’HERMİTT

Pages : 121-134

View : 19 | Download : 14

Publication Date : 2009-06-01

Article Type : Research Paper

Abstract :All rings considered are commutative with 1 and all subrings are unital. If R ⊆ T are rings such that T is a finitely generated R-module, R is not a total quotient ring and insert ignore into journalissuearticles values(R : T); = 0, then there exists a denumerable chain of R-subalgebras of T. The rings having only finite chains of subrings are shown to be the same as the recently classified rings having only finitely many subrings.
Keywords : Commutative ring, ring extension, subalgebra, chain, cardinality, determinant, FIP property, FSP property, integrality, greatest common divisor, pullback, singly generated ring, integral domain, total quotient ring

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