Abstract view
Root closure in Integral Domains, III


Published:19980301
Printed: Mar 1998
David F. Anderson
David E. Dobbs
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Abstract
{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$\}$).
MSC Classifications: 
13G05, 13F25, 13C15, 13F45, 13B99, 12D99 show english descriptions
Integral domains Formal power series rings [See also 13J05] Dimension theory, depth, related rings (catenary, etc.) Seminormal rings None of the above, but in this section None of the above, but in this section
13G05  Integral domains 13F25  Formal power series rings [See also 13J05] 13C15  Dimension theory, depth, related rings (catenary, etc.) 13F45  Seminormal rings 13B99  None of the above, but in this section 12D99  None of the above, but in this section
