FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 209-215

The Jacobson radical of the Laurent series ring

A. A. Tuganbaev

Abstract

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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 $$f of the ring $A$, the Jacobson radical of the skew Laurent series ring $A((x,$f )) is nilpotent and coincides with $N((x,$f )), 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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Last modified: June 17, 2006