1. CMB 2016 (vol 60 pp. 63)
 Chang, Gyu Whan

Power Series Rings Over PrÃ¼fer $v$multiplication Domains, II
Let $D$ be an integral domain, $X^1(D)$ be the set of heightone
prime ideals of $D$,
$\{X_{\beta}\}$ and $\{X_{\alpha}\}$ be
two disjoint nonempty sets of indeterminates over $D$,
$D[\{X_{\beta}\}]$ be the polynomial ring over $D$, and
$D[\{X_{\beta}\}][\![\{X_{\alpha}\}]\!]_1$ be the first type
power series ring over $D[\{X_{\beta}\}]$.
Assume that $D$ is a PrÃ¼fer $v$multiplication domain (P$v$MD)
in which each proper integral $t$ideal has only finitely many
minimal prime ideals
(e.g., $t$SFT P$v$MDs, valuation domains, rings of Krull type).
Among other things, we show that if
$X^1(D) = \emptyset$ or $D_P$ is a DVR for all $P \in X^1(D)$,
then
${D[\{X_{\beta}\}][\![\{X_{\alpha}\}]\!]_1}_{D  \{0\}}$ is a
Krull domain.
We also prove that if $D$ is a $t$SFT P$v$MD, then the complete
integral closure of $D$ is a Krull domain and
ht$(M[\{X_{\beta}\}][\![\{X_{\alpha}\}]\!]_1)$ = $1$ for every
heightone maximal $t$ideal $M$ of $D$.
Keywords:Krull domain, P$v$MD, multiplicatively closed set of ideals, power series ring Categories:13A15, 13F05, 13F25 

2. CMB 1998 (vol 41 pp. 3)
 Anderson, David F.; Dobbs, David E.

Root closure in Integral Domains, III
{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 nroot closed in B[[X]]'' to be equivalent to ``A is nroot
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 onedimensional 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$\}$).
Categories:13G05, 13F25, 13C15, 13F45, 13B99, 12D99 
