Pairs of domains where all intermediate domains are Noetherian

Abstract

For Noetherian integral domains R and T with R S T, (R, T) is called a Noetherian pair (NP) if every domain A, R Q A Q T, is Noetherian.When dim R -1 (Krull dimension) it is shown that the only NP's are those given by the Krull-Akizuki Theorem.For dim R a 2, there is another type of NP besides the finite integral extension, namely (/?, n) where ft =1 li/?"|rk P a 2(.Further, for every NP (/?, T) with dim Ä i2 there is an integral NP extension