ON THE MAXIMAL CARDINALITY OF CHAINS OF INTERMEDIATE RINGS

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 (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.