Geodesic
Root Closure in Integral Domains, III
Canadian mathematical bulletin, Tome 41 (1998) no. 1, pp. 3-9

Voir la notice de l'article provenant de la source Cambridge University Press

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., $S=\{n\in \mathbb{P}\,|\,\,A[[X]]\,\,\text{is}\,n-\text{root}\,\text{closed}\}$ ).
DOI : 10.4153/CMB-1998-001-0
Mots-clés : 13G05, 13F25, 13C15, 13F45, 13B99, 12D99 
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
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