Geodesic
A new characterization of GCD domains of formal power series
Algebra i analiz, Tome 33 (2021) no. 5, pp. 193-206.

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By using the $v$-operation, a new characterization for a power series ring to be a GCD domain is discussed. It is shown that if $D$ is a $\mathrm{UFD}$, then $D[\![X]\!]$ is a GCD domain if and only if for any two integral $v$-invertible $v$‑ideals $I$ and $J$ of $D[\![X]\!]$ such that $(IJ)_{0}\neq (0),$ we have $((IJ)_{0})_{v}$ $= ((IJ)_{v})_{0},$ where $I_0=\{f(0) \mid f\in I\}$. This shows that if $D$ is a GCD domain such that $D[\![X]\!]$ is a $\pi$-domain, then $D[\![X]\!]$ is a GCD domain.
Keywords: GCD domain, power series rings. 
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     title = {A new characterization of {GCD} domains of formal power series},
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A. Hamed. A new characterization of GCD domains of formal power series. Algebra i analiz, Tome 33 (2021) no. 5, pp. 193-206. http://geodesic.mathdoc.fr/item/AA_2021_33_5_a6/

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