Some new results on skew inverse Laurent series rings

Abstract

Let [Formula: see text] be an associative ring equipped with an automorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. Necessary and sufficient conditions are obtained for the skew inverse Laurent series ring [Formula: see text] 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 [Formula: see text].