Let $R$ be an associative ring equipped with an automorphism $\alpha$ and an $\alpha$-derivation $\delta$. Necessary and sufficient conditions are obtained for the skew inverse Laurent series ring $R((x^{-1};\alpha ,\delta ))$ to satisfy a certain ring property which is among being local, semilocal, semiperfect and semisimple, respectively. We also give a characterization of the cleanness of the ring $R((x^{-1};\alpha ,\delta ))$.

中文翻译：

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偏斜逆 Laurent 级数环的一些新结果

让$R$是一个具有自同构的结合环$\alpha$和$\alpha$-推导$\delta$. 得到斜逆Laurent级数环的充要条件$R((X^{-1};\alpha ,\delta ))$满足一定的环性质，分别是局部、半局部、半完全和半单纯。我们还对戒指的清洁度进行了表征$R((X^{-1};\alpha ,\delta ))$.