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Root closure in Integral Domains, III

  • 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 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$\}$).
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
 

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