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# Root closure in Integral Domains, III

Published:1998-03-01
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 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 - 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