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In this paper, we continue to study skew inverse Laurent series ring R((x−1; α,δ)), where R is a ring equipped with an automorphism α and an α-derivation δ. We directly prove that R((x−1; α,δ)) is semiprimitive reduced if and only if R is α-rigid. Also, as an application of our results, by imposing constraints on α and δ, we completely identify the Jacobson radical of R((x−1; α,δ)) whose set of all nilpotent elements has special conditions. Moreover, necessary and sufficient conditions are obtained for the skew inverse Laurent series ring to satisfy a certain ring property which is among being right Artinian, completely primary, right perfect, (semi)local, semiperfect, semiprimary, semiregular, semisimple and strongly regular, respectively. [ABSTRACT FROM AUTHOR]

Let R be an associative ring equipped with an automorphism α and an α -derivation δ. Necessary and sufficient conditions are obtained for the skew inverse Laurent series ring R ((x − 1 ; α , δ)) 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 ; α , δ)). [ABSTRACT FROM AUTHOR]