JP Journal of Algebra, Number Theory and Applications
Abstract: Let Rbe a 2-root closed going-down domain with no factor domain of
characteristic 2. Let Sbe an integral overring of R. Then Sis a going-down domain. If, in addition, Ris quasilocal, then the conductor is a prime ideal of Sand hence (as a prime ideal of R) is unibranched in S, and
the same holds for each prime ideal of Rwhich is contained in I. An example in characteristic with Ras above of arbitrary Krull dimension shows that the unique maximal ideal
of Rneed not be
unibranched in S.
Keywords and phrases: going-down domain, integral extension, overring, prime ideal, unibranched, divided domain, n-root closed, factor domain, Krull dimension, radical function field.
