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Study of skew inverse Laurent series rings

机译：偏斜逆劳伦系列环的研究

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In the present note, we continue the study of skew inverse Laurent series ring R((x?1; α,δ)) and skew inverse power series ring R[[x?1; α,δ]], where R is a ring equipped with an automorphism α and an α-derivation δ. Necessary and sufficient conditions are obtained for R[[x?1; α,δ]] to satisfy a certain ring property which is among being local, semilocal, semiperfect, semiregular, left quasi-duo, (uniquely) clean, exchange, projective-free and I-ring, respectively. It is shown here that R((x?1; α,δ)) (respectively R[[x?1; α,δ]]) is a domain satisfying the ascending chain condition (Acc) on principal left (respectively right) ideals if and only if so does R. Also, we investigate the problem when a skew inverse Laurent series ring R((x?1; α,δ)) has the same Goldie rank as the ring R and is proved that, if R is a semiprime right Goldie ring, then R((x?1; α,δ)) is semiprimitive. Furthermore, we study on the relationship between the simplicity, semiprimeness, quasi-Baerness and Baerness property of a ring R and these of the skew inverse Laurent series ring. Finally, we consider the problem of determining when f(x) ∈ R((x?1; α,δ)) is nilpotent.
机译：在目前的说明中，我们继续研究偏斜逆挥发序列R环R（（x≤1;α，δ）和歪斜逆功率系列环R [[x≤1; α，Δ]]，其中R是配备有万态态α和α-衍生δ的环。 R [[x≤1]获得必要和充分的条件α，Δ]]为了满足局部，半焦，Semiperfect，半法，左准二元，（唯一）清洁，交换，无流程和I形圈之间的某种环形性质。这里示出了R（（x≤1;α，δ））（分别是r [x≤1;α，Δ]）是满足主体上左侧升序（ACC）的域（分别为右）如果也是如此，如果也是如此，那么，我们也研究了偏斜逆奖项系列环R（（x≤1;α，δ）时的问题，并且证明了，如果r是半润右金戒指，然后是R（（x≤1;α，δ））是半像素。此外，我们研究了环R的简单性，半像素，准困难和抗粘性性能与偏斜逆挥发系列环的关系。最后，我们考虑确定何时F（x）∈r（（x≤1;α，δ）的问题是nilpotent。

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