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Search: MSC category 13F25 ( Formal power series rings [See also 13J05] )

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1. 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 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$\}$).

Categories:13G05, 13F25, 13C15, 13F45, 13B99, 12D99

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