Root closure in Integral Domains, III

http://dx.doi.org/10.4153/CMB-1998-001-0
Canad. Math. Bull. 41(1998), 3-9

  Published:1998-03-01
 Printed: Mar 1998

{If A is a subring of a commutative ring B and if n is a positive integer, a number of sufficient conditions are given for ``A[[X]]is n-root closed in B[[X]]'' to be equivalent to ``A is n-root closed in B.'' In addition, it is shown that if S is a multiplicative submonoid of the positive integers ${\bbd P}$ which is generated by primes, then there exists a one-dimensional quasilocal integral domain A (resp., a von Neumann regular ring A) such that $S = \{ n \in {\bbd P}\mid A$ is $n$-root closed$\}$ (resp., $S = \{n \in {\bbd P}\mid A[[X]]$ is $n$-rootclosed$\}$).