Geodesic
The Jacobson radical of the Laurent series ring
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 209-215.

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For a large class of rings $A$ including all rings with right Krull dimension, it is proved that for every automorphism $\varphi$ of the ring $A$, the Jacobson radical of the skew Laurent series ring $A((x,\varphi))$ is nilpotent and coincides with $N((x,\varphi))$, where $N$ is the prime radical of the ring $A$. If $A/N$ is a ring of bounded index, then the Jacobson radical of the Laurent series ring $A((x))$ coincides with $N((x))$. 
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A. A. Tuganbaev. The Jacobson radical of the Laurent series ring. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 209-215. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a14/

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