EXTENSIONS OF INTEGRAL DOMAINS WITH INFINITE CHAINS OF INTERMEDIATE RINGS

摘要

Let R C T be (commutative integral) domains, with corresponding quotient fields K C L. If R≠K, then there exists a denumerable chain of R-subalgebras of T. Examples show that the assertion fails if one deletes either of the assumptions that R≠K or K ≠L or strengthens the "denumerable" part of the conclusion. A partial generalization is given for rings with nontrivial zero-divisors.