Root Closure in Integral Domains, III
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 3-9
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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 $\mathbb{P}$ which is generated by primes, then there exists a one-dimensional quasilocal integral domain $A$ (resp., a von Neumann regular ring $A$ ) such that $S=\{n\in \mathbb{P}|A\,\,\text{is}\,n-\text{root}\,\text{closed}\}$ (resp., $S=\{n\in \mathbb{P}\,|\,\,A[[X]]\,\,\text{is}\,n-\text{root}\,\text{closed}\}$ ).
Anderson, David F.; Dobbs, David E. Root Closure in Integral Domains, III. Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 3-9. doi: 10.4153/CMB-1998-001-0
@article{10_4153_CMB_1998_001_0,
author = {Anderson, David F. and Dobbs, David E.},
title = {Root {Closure} in {Integral} {Domains,} {III}},
journal = {Canadian mathematical bulletin},
pages = {3--9},
year = {1998},
volume = {41},
number = {1},
doi = {10.4153/CMB-1998-001-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-001-0/}
}
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